Tootfinder

From Chiral Topological Dynamics to Chiral Topological Amplification: Real vs Imaginary Parameters in a Hermitian Bosonic Chain
Kiran Babasaheb Estake, T. R. Vishnu, Dibyendu Roy
https://arxiv.org/abs/2508.14560

From Chiral Topological Dynamics to Chiral Topological Amplification: Real vs Imaginary Parameters in a Hermitian Bosonic Chain
We propose a Hermitian quadratic bosonic model (QBH) whose dynamical matrix exhibits distinct topological and dynamical phenomena depending on whether the hopping and pairing amplitudes are real or purely imaginary. In the real-parameter regime, the dynamical matrix is unitarily equivalent to four decoupled copies of the sublattice-symmetric non-Hermitian Su-Schrieffer-Heeger (nSSH2) model, thereby inheriting its topological phases and energy spectrum-including the Möbius phase, a gapless topo…

🇺🇦 #NowPlaying on BBCRadio3's #NewMusicShow
Annette Vande Gorne:
🎵 Imaginary Cityscape
#AnnetteVandeGorne

Estimates for Schr\"{o}dinger Groups and Imaginary Power Operators on Weak Hardy Spaces Associated with Non-negative Self-adjoint Operators and Ball Quasi-Banach Function Spaces
Xiong Liu, Wenhua Wang
https://arxiv.org/abs/2508.13913

Estimates for Schrödinger Groups and Imaginary Power Operators on Weak Hardy Spaces Associated with Non-negative Self-adjoint Operators and Ball Quasi-Banach Function Spaces
Let $(\mathbb{X},d,μ)$ be a doubling metric measure space, $L$ a non-negative self-adjoint operator on $L^2(\mathbb{X})$ satisfying the Davies-Gaffney estimate, and $X(\mathbb{X})$ a ball quasi-Banach function space on $\mathbb{X}$ satisfying some mild assumptions with $p\in(0,\infty)$ and $s_0\in(0,\min\{p,1\}]$. In this article, the authors first study the weak Hardy space $WH_{X,L}(\mathbb{X})$ associated with $L$ and $X(\mathbb{X})$, and then establish the atomic and molecular decompositio…

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Sophia Kennedy:
🎵 Imaginary Friend (Radio Edit)
#NowPlaying #SophiaKennedy
https://sophiakennedy.bandcamp.com/track/imaginary-friend
https://open.spotify.com/track/7CbVZ2Yzl0TtcCERaJDZSR
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Linear response and exact hydrodynamic projections in Lindblad equations with decoupled Bogoliubov hierarchies
Patrik Penc, Fabian H. L. Essler
https://arxiv.org/abs/2507.13867

Linear response and exact hydrodynamic projections in Lindblad equations with decoupled Bogoliubov hierarchies
We consider a class of spinless-fermion Lindblad equations that exhibit decoupled BBGKY hierarchies. In the cases where particle number is conserved, their late time behaviour is characterized by diffusive dynamics, leading to an infinite temperature steady state. Some of these models are Yang-Baxter integrable, others are not. The simple structure of the BBGKY hierarchy makes it possible to map the dynamics of Heisenberg-picture operators on few-body imaginary-time Schrödinger equations with …

A class number problem for imaginary cyclic number fields of 2-power degrees
St\'ephane R. Louboutin
https://arxiv.org/abs/2508.10563 https://arxiv.org…

A class number problem for imaginary cyclic number fields of 2-power degrees
In 2024, M. K. Ram proved that the class number of an imaginary cyclic quartic number field is never equal to a prime $p\equiv 3\pmod 4$. Here we greatly generalize this result to the case of the non-quadratic imaginary cyclic number fields of $2$-power degrees and not necessarily prime class numbers.

Norm-Stabilized Imaginary-Time Evolution via Feedback Control
Stylianos Savva
https://arxiv.org/abs/2507.11700 https://arxiv.org/pdf/…

Norm-Stabilized Imaginary-Time Evolution via Feedback Control
We present a norm-stabilized imaginary-time evolution (ITE) scheme for the one-dimensional nonlinear Schrodinger equation (NLSE). Traditional ITE solvers often require explicit renormalization of the wavefunction after each step to preserve norm, which can be disruptive and algorithmically inflexible. We propose an alternative approach in which the evolution is continuously stabilized using an adaptive feedback term mu(tau), proportional to the time derivative of the wavefunction norm. This res…

🫥 Imaginary athletes: Creating make-believe teammates, competitors and coaches during play
https://theconversation.com/imaginary-athletes-creating-make-believe-teammates-competitors-and-coaches-during-play-254879

Imaginary athletes: Creating make-believe teammates, competitors and coaches during play
Imagination is a fundamental tool for everyday life. Unsurprisingly, many kids harness it during athletic play, conjuring a fun teammate, a supportive coach or a worthy opponent.

Twisted Dirac operators and fractional correlations of the massless sine-Gordon model at the free fermion point
Roland Bauerschmidt, Scott Mason, Christian Webb
https://arxiv.org/abs/2508.14806

Twisted Dirac operators and fractional correlations of the massless sine-Gordon model at the free fermion point
For the massless sine-Gordon model at the free fermion point, in infinite volume, we define the fractional (charge or vertex operator) correlation functions from the probabilistic path integral and prove that they are given by renormalized determinants of massive twisted Dirac operators. The fractional correlation functions are the moments of the imaginary multiplicative chaos, a random generalized function that we construct with respect to the infinite-volume massless sine-Gordon measure. The …

On the electronic normal modes of the Meyer-Miller-Stock-Thoss representation of non-adiabatic dynamics
Lauren E. Cook (University College London), Timothy J. H. Hele (University College London)
https://arxiv.org/abs/2508.14775

On the electronic normal modes of the Meyer-Miller-Stock-Thoss representation of non-adiabatic dynamics
Accurate and efficient simulation of non-adiabatic dynamics is highly desirable for understanding charge and energy transfer in complex systems. A key criterion for obtaining an accurate method is conservation of the Quantum Boltzmann Distribution (QBD). For a single surface, Matsubara dynamics is known to conserve the QBD, as a consequence of truncating the dynamics in the higher normal modes of the imaginary-time path integral. Recently, a Non-Adiabatic Matsubara (NA-Mats) dynamics has been p…

Imaginary dialog:
"Excuse me, where is the train station?"
"It's these unmarked doors between the barber shop and the driving school."
#Głogów, #Poland.
#rail

Exact kinetic propagators for coherent state complex Langevin simulations
Thomas G. Kiely, Ethan C. McGarrigle, Glenn H. Fredrickson
https://arxiv.org/abs/2508.11057 https://

Exact kinetic propagators for coherent state complex Langevin simulations
We introduce and benchmark an improved algorithm for complex Langevin simulations of bosonic coherent state path integrals. Our approach utilizes a Strang splitting of the imaginary-time propagator rather than the conventional linear-order Taylor expansion, allowing us to construct an action that incorporates higher-order terms at negligible computational cost. The resulting algorithm enjoys guaranteed linear stability independent of the imaginary-time discretization, enabling more resource-eff…

Semi-Riemannian $\text{spin}^c$ manifolds carrying generalized Killing spinors and the classification of Riemannian $\text{spin}^c$ manifolds admitting a type I imaginary generalized Killing spinor
Samuel Lockman
https://arxiv.org/abs/2509.08477

Semi-Riemannian $\text{spin}^c$ manifolds carrying generalized Killing spinors and the classification of Riemannian $\text{spin}^c$ manifolds admitting a type I imaginary generalized Killing spinor
We classify Riemannian $\text{spin}^c$ manifolds carrying a type I imaginary generalized Killing spinor, by explicitly constructing a parallel spinor on each leaf of the canonical foliation given by the Dirac current. We also provide a class of Riemannian $\text{spin}^c$ manifolds carrying a type II imaginary generalized Killing spinor, by considering spacelike hypersurfaces of Lorentzian $\text{spin}^c$ manifolds. We carry out much of the work in the setting of semi-Riemannian $\text{spin}^c$-…

Saturable Quantum Speed Limits for Imaginary-Time Evolution
Kohei Kobayashi
https://arxiv.org/abs/2508.10361 https://arxiv.org/pdf/2508.10361

Saturable Quantum Speed Limits for Imaginary-Time Evolution
We derive a Geometric quantum speed limit (QSL) for imaginary-time evolution, where the dynamics is governed by a non-unitary Schrödinger equation. By introducing a cost function based on the angular distance between the normalized evolving state and the initial state, we obtain a lower bound on the evolution time expressed as the ratio between this angle and the time-averaged energy dispersion. Our bound is analytical, general, and applicable to arbitrary time-independent Hamiltonians. We ana…

Emergent momentum-space topological pseudospin defects in non-Hermitian systems
Yow-Ming Robin Hu, Elena A. Ostrovskaya, Alexander Yakimenko, Eliezer Estrecho
https://arxiv.org/abs/2509.14605

Emergent momentum-space topological pseudospin defects in non-Hermitian systems
Topological defects are central to modern physics, from spintronics to photonics, due to their robustness and potential application in information processing. In this work, we discuss topological point defects that spontaneously emerge at the imaginary Fermi arcs (degeneracy lines) in momentum space of two-dimensional systems described by non-Hermitian effective Hamiltonians. In particular, we consider a generic non-Hermitian Dirac model and a phenomenological model describing hybrid light-matt…

🇺🇦 Auf radioeins läuft...
Sophia Kennedy:
🎵 Imaginary Friend (Radio Edit)
#NowPlaying #SophiaKennedy
https://sophiakennedy.bandcamp.com/track/imaginary-friend
https://open.spotify.com/track/7CbVZ2Yzl0TtcCERaJDZSR

Melting down a tetraquark: $D^{\ast}D^{(\ast)}$ interactions and $T_{cc}(3875)^ $ in a hot environment
Victor Montesinos, Gloria Montana, Miguel Albaladejo, Juan Nieves, Laura Tolos
https://arxiv.org/abs/2507.13319

Melting down a tetraquark: $D^{\ast}D^{(\ast)}$ interactions and $T_{cc}(3875)^+$ in a hot environment
We discuss the modification of the properties of the tetraquark-like $T_{cc}(3875)^+$ and its heavy quark spin partner, $T_{cc}(4016)^{*+}$ immersed in a hot bath of pions. We consider these exotic states as purely isoscalar $DD^\ast$ and $D^\ast D^\ast$ $S$-wave bound states, respectively. Finite temperature effects are incorporated through the $D$ and $D^\ast$ state-of-the-art thermal spectral functions calculated in [G. Montana et al., Phys. Rev. D, 102 (2020) 096020], using the imaginary-ti…

Hilbert spaces admit no finitary discrete imaginaries
Ruiyuan Chen, Isabel Trindade
https://arxiv.org/abs/2509.11321 https://arxiv.org/pdf/2509.11321

Hilbert spaces admit no finitary discrete imaginaries
We prove that every functor from the category of Hilbert spaces and linear isometric embeddings to the category of sets which preserves directed colimits must be essentially constant on all infinite-dimensional spaces. In other words, every finitary set-valued imaginary over the theory of Hilbert spaces, in a broad signature-independent sense, must be essentially trivial. This extends a result and answers a question by Lieberman--Rosický--Vasey, who showed that no such functor on the supercate…

Levinson's theorem for dissipative systems, or how to count the asymptotically disappearing states
A. Alexander, J. Faupin, S. Richard
https://arxiv.org/abs/2509.12799 https…

Levinson's theorem for dissipative systems, or how to count the asymptotically disappearing states
We consider dissipative Schroedinger operators of the form $H=-Δ+V(x)$ on $L^2(\mathbb R^3)$, with $V(x)$ a complex, bounded and decaying potential with a non-positive imaginary part. We prove a topological version of Levinson's theorem corresponding to an index theorem for the discrete, complex spectrum of $H$.

The $p$-adic valuation of local resolvents, generalized Gauss sums and anticyclotomic Hecke $L$-values of imaginary quadratic fields at inert primes
Ashay Burungale, Shinichi Kobayashi, Kazuto Ota
https://arxiv.org/abs/2507.08221

The $p$-adic valuation of local resolvents, generalized Gauss sums and anticyclotomic Hecke $L$-values of imaginary quadratic fields at inert primes
We prove an asymptotic formula for the $p$-adic valuation of Hecke $L$-values of an imaginary quadratic field at an inert prime $p$ along the anticyclotomic $\mathbb{Z}_p$-tower. The key is determination of the $p$-adic valuation of generalized Gauss sums defined using Coates-Wiles homomorphism, and of local resolvents in $\mathbb{Z}_p$-extensions. This answers a question of Rubin.

Scalable tensor network algorithm for quantum impurity problems
Zhijie Sun, Ruofan Chen, Zhenyu Li, Chu Guo
https://arxiv.org/abs/2507.12722 https://

Scalable tensor network algorithm for quantum impurity problems
The Grassmann time-evolving matrix product operator method has shown great potential as a general-purpose quantum impurity solver, as its numerical errors can be well-controlled and it is flexible to be applied on both the imaginary- and real-time axis. However, a major limitation of it is that its computational cost grows exponentially with the number of impurity flavors. In this work, we propose a multi-flavor extension of it to overcome this limitation. The key insight is that to calculate m…

Bounded imaginary powers of generalized diffusion operators
Alexandre Thorel (LMAH)
https://arxiv.org/abs/2509.03105 https://arxiv.org/pdf/2509.03105

Bounded imaginary powers of generalized diffusion operators
In this paper, we investigate the boundedness of the imaginary powers of four generalized diffusion operators. This key property, which implies the maximal regularity property, allows us to solve both the linear and semilinear Cauchy problems associated with each operator. Our approach relies on semigroup theory, functional calculus, operator sum theory and R-boundedness techniques to establish the boundedness of the imaginary powers of generalized diffusion operators. We then apply the Dore-Ve…

Momentum expansions in finite-density perturbative calculations
Mika Nurmela, Juuso \"Osterman
https://arxiv.org/abs/2508.10623 https://arxiv.org/pdf/…

Momentum expansions in finite-density perturbative calculations
Complex-valued Feynman integrals in the imaginary time formalism and zero-temperature limit suffer from particular types of infrared divergences that can not be regulated by integration dimension alone. Related problems leading to integration order dependent results are even further pronounced in the presence of additional scales such as external momenta. This plays a noticeable role in systems featuring fermionic degrees of freedom such as cold Quantum Chromodynamics, where loop integrals are …

Partially Alternative Real Division Algebras With A Few Imaginary Units
Tianran Hua, Marina Tvalavadze
https://arxiv.org/abs/2507.04919 https://

Partially Alternative Real Division Algebras With A Few Imaginary Units
In this paper, we extend the investigation of four-dimensional partially alternative algebras $\mathcal A$ initiated in \cite{HNT}. The partial alternativity condition, a natural generalization of the alternativity axiom, broadens the class of alternative algebras, enabling the exploration of non-associative structures with weakened algebraic constraints. We focus on four-dimensional partially alternative real division algebras (RDAs) equipped with at least three distinct imaginary units and …

I, too, am capable of drawing “maps” of imaginary places that do not and never will exist, which I am neither capable of building nor genuinely intending to build.
Can I please have billions of dollars too? thx https://fed.brid.gy/r/https://bsky.app/profile/did:plc:hljkd4e73ttz5xjjywsvebzz/post/3ly4d5fspub2r

Quasinormal modes and tidal Love numbers of covariant effective quantum black holes with cosmological constant
Yunlong Liu, Xiangdong Zhang
https://arxiv.org/abs/2509.12013 http…

Quasinormal modes and tidal Love numbers of covariant effective quantum black holes with cosmological constant
This paper systematically investigates the quasinormal modes (QNMs) and tidal Love numbers of covariant quantum-modified black holes (BHs) within two cosmological constant-dependent metric frameworks. By deriving axial/polar perturbation equations and employing pseudospectral methods (for QNMs) and numerical integration (for Love numbers), we quantify the quantum parameter $ζ$'s influence. We find that, higher overtones exhibit enhanced $ζ$ sensitivity. Solution 1 maintains purely imaginary Q…

"Acting is behaving truthfully under imaginary circumstances."
-Sanford Meisner
#acting #coaching #inspiration

Carrier Density Dependence of Superconducting Transition Temperature in Electron-doped $\rm{SrTiO_3}$ Based on the First-principles Calculations
Riku Ikaida, Kazuhiro Sano, Yoshimi Masuda, Takuya Sekikawa, Yoshiaki \=Ono
https://arxiv.org/abs/2509.10881

Carrier Density Dependence of Superconducting Transition Temperature in Electron-doped $\rm{SrTiO_3}$ Based on the First-principles Calculations
Electron-doped strontium titanate $\rm{SrTiO_3}$, known to be one of the most dilute superconductors, is investigated on the basis of the first-principles calculations. When the carrier density n decreases, the frequencies of the ferroelectric optical phonons near the $Γ$-point monotonically decreases in the overdoped regime with $n<10^{20}/\rm{cm}^{3}$, while unphysical imaginary phonon frequencies due to ferroelectric instabilities appear in the underdoped regime with $n>10^{20}/\rm{cm}^{3}$…

So you've been following the Skydance/Paramount merger. Did you know about administration's claim they were getting $20m in PSAs? Another not widely publicized story: Trump did this successfully with the Qatari jet. The United States was talking to Qatar about leasing or buying, but then Trump wished aloud that maybe it could be a gift . . . and then it was a gift. We're getting dangerously close to "Will no one rid me of this meddlesome priest?" territory.
Been d…

Class groups of imaginary quadratic points on $X_1(16)$
Maarten Derickx
https://arxiv.org/abs/2507.04604 https://arxiv.org/pdf/2507.0…

Class groups of imaginary quadratic points on $X_1(16)$
The main result is to show that if $K \ncong \mathbb Q(\sqrt{-15})$ is an imaginary quadratic field and $E$ is an elliptic curve over $K$ with a torsion point of order 16, then the class number of $K$ is divisible by 10. This gives an affirmative answer to a 12 year old question by David Krumm. This is done by setting up a more general framework for studying divisibility of class groups of imaginary quadratic points on hyper-elliptic curves and applying it to $X_1(16)$.

High-precision baryon number cumulants from lattice QCD in a finite box: cumulant ratios, Lee-Yang zeros and critical endpoint predictions
Alexander Adam, Szabolcs Bors\'anyi, Zoltan Fodor, Jana N. Guenther, Piyush Kumar, Paolo Parotto, Attila P\'asztor, Chik Him Wong
https://arxiv.org/abs/2507.13254

High-precision baryon number cumulants from lattice QCD in a finite box: cumulant ratios, Lee-Yang zeros and critical endpoint predictions
We have performed high-statistics lattice simulations using 4HEX improved staggered fermions on $16^3 \times 8$ lattices. We calculated the Taylor expansion coefficients of the pressure with respect to the baryochemical potential to the tenth order at zero, and fourth order at purely imaginary chemical potentials. We used this data to construct rational function approximations of the free energy. We use a rational ansatz that explicitly satisfies the charge conjugation symmetry and the Roberge-…

Sculpting Topological Modes on Photonic Chips by Artificial Gauge Fields
Zhiyuan Lin, Jian Li, Wange Song, Xueyun Li, Haoran Xin, Xian Long, Chen Chen, Shining Zhu, Tao Li, Shuang Zhang
https://arxiv.org/abs/2509.10315

Sculpting Topological Modes on Photonic Chips by Artificial Gauge Fields
Significant efforts have been devoted to manipulating topological states, which often manifest as localized modes at interfaces between distinct topological phases. In this work, we demonstrate a versatile approach to sculpting topological modes (TMs) into any desired shapes by incorporating various artificial gauge fields (AGFs), including scalar, vector, and imaginary gauge potentials, and leveraging the power of artificial neural networks (ANNs). These AGFs enable precise tuning of the dissi…

🇺🇦 Auf radioeins läuft...
Sophia Kennedy:
🎵 Imaginary Friend (Radio Edit)
#NowPlaying #SophiaKennedy
https://sophiakennedy.bandcamp.com/track/imaginary-friend
https://open.spotify.com/track/7CbVZ2Yzl0TtcCERaJDZSR

Formal verification for robo-advisors: Irrelevant for subjective end-user trust, yet decisive for investment behavior?
Alina Tausch, Magdalena Wischnewski, Mustafa Yalciner, Daniel Neider
https://arxiv.org/abs/2509.08540

Formal verification for robo-advisors: Irrelevant for subjective end-user trust, yet decisive for investment behavior?
This online-vignette study investigates the impact of certification and verification as measures for quality assurance of AI on trust and use of a robo-advisor. Confronting 520 participants with an imaginary situation where they were using an online banking service to invest their inherited money, we formed 4 experimental groups. EG1 achieved no further information of their robo-advisor, while EG2 was informed that their robo-advisor was certified by a reliable agency for unbiased processes, an…

There's another layer to this as well, I think. Any social media feed interlaces horrible things with wonderful things in a completely contextually devoid list. A funny cat picture and a traumatic picture or video of violence are both "rated" in the same way, with the same imaginary internet points, without any differentiation between good and bad.
I feel like this is also cooking our brains a bit.

Cutting rules for non-relativistic dark matter in solids based on Kohn-Sham orbitals
Zheng-Liang Liang, Fawei Zheng
https://arxiv.org/abs/2507.11033 https:…

Cutting rules for non-relativistic dark matter in solids based on Kohn-Sham orbitals
The Cutkosky cutting rules establish a direct connection between the imaginary parts of loop amplitudes and physical observables such as decay rates and cross sections, providing heuristic insights into the underlying processes. This work lays a robust theoretical foundation for the application of cutting rules in solid-state systems involving instantaneous dark matter (DM)-electron Yukawa interaction as well as the Coulomb potential. The cutting rules are formulated using the single-electron w…

Quantum Imaginary-Time Evolution with Polynomial Resources in Time
Lei Zhang, Jizhe Lai, Xian Wu, Xin Wang
https://arxiv.org/abs/2507.00908 https://…

Quantum Imaginary-Time Evolution with Polynomial Resources in Time
Imaginary-time evolution is fundamental to analyzing quantum many-body systems, yet classical simulation requires exponentially growing resources in both system size and evolution time. While quantum approaches reduce the system-size scaling, existing methods rely on heuristic techniques with measurement precision or success probability that deteriorates as evolution time increases. We present a quantum algorithm that prepares normalized imaginary-time evolved states using an adaptive normaliza…

PSA: 🥵 Idk who needs to hear this, but in a heatwave for the love of science use air conditioning. If you don’t have air conditioning, get a portable unit as soon as possible.
The climate is going to get hotter and heat can very easily kill you or a loved one or a pet; or cause permanent disability.
Heat is a lot more dangerous than cold temperatures; even if you’re “young and healthy”.
The climate is already fucked and has long reached a tipping point as far as humans go—our only bet is large-scale CO2 extraction.
Sacrificing your health “to save energy*” for an imaginary fight that we have already lost is stupid. It’s also one of those “individual responsibility” mindfucks—the culprits for pollution are industry maximizing profits and governments that are not acting.
Anyway, stay cool.
*note that AC uses overall a lot less energy than heating does

🇺🇦 #NowPlaying on KEXP's #VarietyMix
Burial:
🎵 Imaginary Festival
#Burial
https://burial.bandcamp.com/track/comafields
https://open.spotify.com/track/7D7TSZtL7TUqO10uyr0Dih

Nagell-Lutz theorem for imaginary quadratic fields of class number one
Leena Mondal, Amrutha C
https://arxiv.org/abs/2509.07524 https://arxiv.org/pdf/2509.…

Nagell-Lutz theorem for imaginary quadratic fields of class number one
We prove the Nagell-Lutz theorem for the imaginary quadratic fields of class number one.

🇺🇦 Auf #radioeins läuft...
Sophia Kennedy:
🎵 Imaginary Friend (Radio Edit)
#NowPlaying #SophiaKennedy
https://sophiakennedy.bandcamp.com/track/imaginary-friend
https://open.spotify.com/track/7CbVZ2Yzl0TtcCERaJDZSR

Now Claudio Cattaneo (Barcelona).
Limits are both material and constructed, in a dialectical relationship.
This time the cause of the coming collapse is the shift of imaginary of the good life.
We have agency to make the change - don't just wait for governments to make the change.

Sonnet 027 - XXVII
Weary with toil, I haste me to my bed,
The dear repose for limbs with travel tired;
But then begins a journey in my head
To work my mind, when body's work's expired:
For then my thoughts--from far where I abide--
Intend a zealous pilgrimage to thee,
And keep my drooping eyelids open wide,
Looking on darkness which the blind do see:
Save that my soul's imaginary sight
Presents thy shadow to my sightless…

An infinite family of pairs of distinct quartic Galois CM-fields with the same discriminant and regulator
Yoshichika Iizuka, Yutaka Konomi
https://arxiv.org/abs/2506.23541

An infinite family of pairs of distinct quartic Galois CM-fields with the same discriminant and regulator
We construct an infinite family of pairs of distinct imaginary biquadratic fields and pairs of distinct imaginary cyclic quartic fields with the same discriminant and regulator. We also construct an infinite family of imaginary biquadratic fields and imaginary cyclic quartic fields with the same regulator. Moreover, we give examples of a pair of distinct imaginary biquadratic fields and a pair of distinct imaginary cyclic quartic fields with the same discriminant, regulator and class number.

Quiver varieties and root multiplicities in rank 3
Patrick Chan, Peter Tingley
https://arxiv.org/abs/2508.04804 https://arxiv.org/pdf/2508.04804

Quiver varieties and root multiplicities in rank 3
Building on our previous work in rank two, we use quiver varieties to give a combinatorial upper bound on dimensions of certain imaginary root spaces for rank 3 symmetric Kac-Moody algebras. We describe an explicit method for extracting combinatorics when the Dynkin diagram is bipartite (i.e. two of the nodes are not connected). As in rank two we believe these bounds are quite tight and we give computational evidence to this effect, although there is more error in rank 3 than in rank 2.

Null geodesics, causal structure, and matter accretion in Lorentzian-Euclidean black holes
Salvatore Capozziello, Emmanuele Battista, Silvia De Bianchi
https://arxiv.org/abs/2507.08431

Null geodesics, causal structure, and matter accretion in Lorentzian-Euclidean black holes
Recently, we introduced the Lorentzian-Euclidean black hole, a static and spherically symmetric solution of vacuum Einstein equations that exhibits a change in metric signature across the event horizon. In this framework, the analysis of radial trajectories of freely falling bodies proves that the central singularity can be avoided via a mechanism we interpret as atemporality, which is responsible for the shift of the time variable from real to imaginary values. In this paper, we further expl…

🇺🇦 Auf radioeins läuft...
Sophia Kennedy:
🎵 Imaginary Friend (Radio Edit)
#NowPlaying #SophiaKennedy
https://sophiakennedy.bandcamp.com/track/imaginary-friend
https://open.spotify.com/track/7CbVZ2Yzl0TtcCERaJDZSR

Quantum Pontus-Mpemba Effects in Real and Imaginary-time Dynamics
Hui Yu, Jiangping Hu, Shi-Xin Zhang
https://arxiv.org/abs/2509.01960 https://arxiv.org/pd…

Quantum Pontus-Mpemba Effects in Real and Imaginary-time Dynamics
The quantum Pontus-Mpemba effect (QPME) is a counterintuitive phenomenon wherein a quantum system relaxes more rapidly through a two-step evolution protocol than through direct evolution under a symmetric Hamiltonian alone. In this protocol, the system first evolves under a symmetry-breaking Hamiltonian and then switches to a symmetric one. We demonstrate that QPME occurs under both real-time and imaginary-time dynamics with respect to $U(1)$-symmetry. Using tilted ferromagnetic initial states,…

Replaced article(s) found for cs.ET. https://arxiv.org/list/cs.ET/new
[1/1]:
- Classical optimization with imaginary time block encoding on quantum computers: The MaxCut problem
Dawei Zhong, Akhil Francis, Ermal Rrapaj

"Acting is behaving truthfully under imaginary circumstances."
-Sanford Meisner
#acting #coaching #inspiration

A folded string dual for the Sachdev-Ye-Kitaev model
David Vegh
https://arxiv.org/abs/2509.05435 https://arxiv.org/pdf/2509.05435

A folded string dual for the Sachdev-Ye-Kitaev model
We propose a folded string moving in rigid AdS$_2$ with imaginary radius squared as a dual of the Sachdev-Ye-Kitaev (SYK) model at its conformal fixed point. In standard AdS$_2$, the string is represented by two massless particles connected by straight string segments. The particles move at the speed of light, abruptly reversing direction at turning points. We describe the system using the lightcone coordinates of these points, with the Poisson structure obtained from the Peierls bracket. In Ad…

$w$-mode oscillation of neutron star in a new relativistic hybrid model
D. Dey, Jeet Amrit Pattnaik, R. N. Panda, S. K. Patra
https://arxiv.org/abs/2509.01175 https://

$w$-mode oscillation of neutron star in a new relativistic hybrid model
We investigate how the pulsation frequencies of axial gravitational-wave modes ($w$-modes) in a non-rotating neutron star depend on its composition, particularly when including quarkyonic matter and fermionic dark matter. These modes emerge from the coupling between the star's fluid component and the gravitational field of general relativity, which are highly damped and characterized by complex frequencies with comparable real and imaginary parts. Using a relativistic mean field formalism for t…

Got all of my #BandcampFriday purchases in, with 1hr left to spare! 😅
✨ My highlights:
kompany by mote booker, smino & phoelix: https://montebooker.bandcamp.com/track/…

Density of solutions for systems of forms
Amichai Lampert
https://arxiv.org/abs/2507.11514 https://arxiv.org/pdf/2507.11514

Density of solutions for systems of forms
Let $K$ be a field of characteristic zero over which every diagonal form in sufficiently many variables admits a nontrivial solution. For example, $K$ may be a totally imaginary number field or a finite extension of a $p$-adic field. Suppose $f_1,\ldots,f_s$ are forms of degree $d$ over $K.$ Bik, Draisma and Snowden recently proved that there exists a constant $B = B(d,s,K)$ such that the rational solutions to the system of equations $f_1=\ldots=f_s = 0$ are Zariski dense, as long as the Birch …

Algorithmic methods of finite discrete structures. Topological graph drawing (part IV)
Sergey Kurapov, Maxim Davidovsky
https://arxiv.org/abs/2507.16759 ht…

Algorithmic methods of finite discrete structures. Topological graph drawing (part IV)
The chapter presents mathematical models intended for creating a topological drawing of a non-separable non-planar graph based on the methods of G. Ringel's vertex rotation theory. The induced system of cycles generates a topological drawing of a certain thickness. A method for determining the location of imaginary vertices by finding the intersection of connections on a plane is presented. A topological drawing of a maximum planar subgraph is used as a basis.

Polarizability of a Wigner crystal
Navinder Singh
https://arxiv.org/abs/2509.07590 https://arxiv.org/pdf/2509.07590…

Polarizability of a Wigner crystal
We present a calculation of the imaginary part of the polarizability of a Wigner crystal using the Fluctuation-Dissipation theorem. The oscillations of the localized electrons about their equilibrium positions are treated in the harmonic approximation and the electric dipole-moment -- dipole-moment correlator is computed by a normal mode expansion. The amplitudes and phases of the different normal modes are assumed to be statistically independent. In the first case, polarizability is computed i…

Relation between semigroup growth and resolvent decay for immediately differentiable semigroups
Masashi Wakaiki
https://arxiv.org/abs/2507.01474 https://…

Relation between semigroup growth and resolvent decay for immediately differentiable semigroups
We study rates of growth of $\|AT(t)\|$ as $t \downarrow 0$ for an immediately differentiable $C_0$-semigroup $(T(t))_{t \geq 0}$ with generator $A$. We assume that the resolvent of the semigroup generator decays on the imaginary axis at rates described by functions of positive increase, which enable estimates on scales finer than polynomial ones. First, in the Banach space setting, we present lower and upper bounds for the semigroup growth. Next, we improve the upper estimate for Hil…

Temperature-induced measurement sensitivity enhancement via imaginary weak values
Lorena Ballesteros Ferraz, Alexandre Matzkin, Alok Kumar Pan
https://arxiv.org/abs/2509.04048 h…

Temperature-induced measurement sensitivity enhancement via imaginary weak values
We investigate the potential of weak measurement and post-selection to enhance measurement sensitivity when the initial probe state is mixed. In our framework, the mixedness of the probe's density operator is controlled by temperature. We focus on two key quantities: the signal-to-noise ratio and the quantum Fisher information of the final probe state, evaluated after post-selection is applied on the system. Our analysis employs a rigorous, all-order coupling treatment of measurement, demonstra…

Generalized Rellich's lemmas, uniqueness theorem and inside-out duality for scattering poles
Xiaodong Liu, Jiguang Sun, Lei Zhang
https://arxiv.org/abs/2507.04242

Generalized Rellich's lemmas, uniqueness theorem and inside-out duality for scattering poles
Scattering poles correspond to non-trivial scattered fields in the absence of incident waves and play a crucial role in the study of wave phenomena. These poles are complex wavenumbers with negative imaginary parts. In this paper, we prove two generalized Rellich's lemmas for scattered fields associated with complex wavenumbers. These lemmas are then used to establish uniqueness results for inverse scattering problems. We further explore the inside-out duality, which characterizes scattering po…

Nonlocal nucleon-nucleus optical potentials from chiral effective field theory
Laina M. Stahulak, Jeremy W. Holt
https://arxiv.org/abs/2509.04665 https://a…

Nonlocal nucleon-nucleus optical potentials from chiral effective field theory
We investigate the nonlocality in microscopic optical potentials derived from chiral effective field theory. For this purpose we employ the Perey-Buck ansatz, which connects the energy dependence of purely local optical potentials to a Gaussian spatial nonlocality. We find that the dominant source of energy dependence in the microscopic real optical potential indeed arises from spatial nonlocalities, while the energy dependence associated with the microscopic imaginary optical potential is a ge…

Magnetism from Conductors, and Enhanced Non-Linear Phenomena
JB Pendry, AJ Holden, DJ Robbins, WJ Stewart
https://arxiv.org/abs/2507.01680 https://

Magnetism from Conductors, and Enhanced Non-Linear Phenomena
We show that microstructures built from non-magnetic conducting sheets exhibit an effective magnetic permeability, /mu_meff, which can be tuned to values not accessible in naturally occurring materials, including large imaginary components of /mu_meff. The microstructure is on a scale much less than the wavelength of radiation, is not resolved by incident microwaves, and uses a very low density of metal so that structures can be extremely lightweight. Most of the structures are resonant due to …

Imaginary scaling
P. M. Ferreira, B. Grzadkowski, O. M. Ogreid
https://arxiv.org/abs/2506.21145 https://arxiv.org/pdf/2506.21145

Imaginary scaling
Recently, a hitherto unknown class of RG-stable relations between parameters of bosonic field theories have been identified and dubbed as the r0 or 'GOOFy' symmetries. Here, 1-loop properties of the r0 invariant 2-Higgs Doublet Model and a minimal symmetric model are discussed. It is concluded that the symmetry is present at the 1-loop provided the UV cut-off squared transforms non-trivially under r0. The minimal model requires the presence of two real fields.

Subwavelength Localisation in Nonreciprocal Disordered Systems
Habib Ammari, Silvio Barandun, Clemens Thalhammer, Alexander Uhlmann
https://arxiv.org/abs/2507.02096

Subwavelength Localisation in Nonreciprocal Disordered Systems
We investigate the competing mechanisms of localisation in one-dimensional disordered block subwavelength resonator systems subject to nonreciprocal damping, induced by an imaginary gauge potential. Using a symmetrisation approach to enable the adaptation of tools from Hermitian systems, we derive the limiting spectral distribution of these systems as the number of blocks goes to infinity and characterise their spectral properties in terms of the spectral properties of their constituent blocks.…

Persistent Charge and Spin Currents in a Ferromagnetic Hatano-Nelson Ring
Sourav Karmakar, Sudin Ganguly, Santanu K. Maiti
https://arxiv.org/abs/2509.06109 https://

Persistent Charge and Spin Currents in a Ferromagnetic Hatano-Nelson Ring
We investigate persistent charge and spin currents in a ferromagnetic Hatano-Nelson ring with anti-Hermitian intradimer hopping, where non-reciprocal hopping generates a synthetic magnetic flux and drives a non-Hermitian Aharonov-Bohm effect. The system supports both real and imaginary persistent currents, with ferromagnetic spin splitting enabling all three spin-current components, dictated by the orientation of magnetic moments. The currents are computed using the current operator method with…

Excitonic skin effect
Wenhui Xu, Qi Zhou
https://arxiv.org/abs/2508.20027 https://arxiv.org/pdf/2508.20027

Excitonic skin effect
We show that strong interactions combined with band-dependent imaginary vector potentials give rise to boundary localization of particle-hole pairs, which we term the excitonic skin effect. In a bilayer system with layer-specific gain/loss and an in-plane magnetic field, excitons experience a net imaginary vector potential, resulting in directional amplification of particle-hole pairs. Including nearest-neighbor interactions leads to a non-Hermitian bosonic Kitaev model, where the pairing effec…

Regulators of the fixed elliptic curve over rank-one imaginary quadratic fields
Shenghao Hua
https://arxiv.org/abs/2507.20297 https://arxiv.org/pdf/2507.20…

Regulators of the fixed elliptic curve over rank-one imaginary quadratic fields
We establish a one-sided central limit theorem for the logarithms of regulators of a fixed rational non-CM elliptic curve $E$ over imaginary quadratic fields of rank one, motivated by the Gross--Zagier formula and a result of Radziwiłłand Soundararajan. We also establish the existence of many imaginary quadratic fields whose regulators grow at least as fast as the square root of the conductor of the field. When the central value of the $L$-function of $E$ is non-vanishing, these results a…

Spontaneous collapse effects on relativistic fermionic matter
Y. M. P. Gomes
https://arxiv.org/abs/2509.04585 https://arxiv.org/pdf/2509.04585

Spontaneous collapse effects on relativistic fermionic matter
This study expands the spontaneous collapse assumptions into the relativistic quantum field theory framework for Dirac fields. By solving Lindblad's master equation using the Keldysh formalism, the effective action is derived, which captures the dynamics of fermions with spontaneous collapse represented as an imaginary self-interaction term. Utilizing the corresponding Dyson-Schwinger equations at 1-loop approximation, the effective mass induced by the nonlinearity is computed. The findings ind…

🇺🇦 Auf radioeins läuft...
Sophia Kennedy:
🎵 Imaginary Friend (Radio Edit)
#NowPlaying #SophiaKennedy
https://sophiakennedy.bandcamp.com/track/imaginary-friend
https://open.spotify.com/track/7CbVZ2Yzl0TtcCERaJDZSR

Complex Band Structures and Bound States in the Continuum: A Unified Theoretical Framework
Jie Liu, Ziyun Peng, Qianju Song, Ang Chen, Liping Yang, Chunxiong Zheng, Dezhuan Han
https://arxiv.org/abs/2509.03163

Complex Band Structures and Bound States in the Continuum: A Unified Theoretical Framework
Complex band structures describe resonant modes in periodic systems finite in one direction, crucial for applications in photonics like sensors and lasers. The imaginary frequency component, $ω''$, tied to quality factors, is often probed through numerical or phenomenological models, limiting deeper insights. Here, we introduce a first-principles framework deriving complex band structures from scattering matrix poles, integrated with perturbation theory to define minimal Hilbert spaces based o…

Testing frozen-in pNGB dark matter with a long-lived dark Higgs
Nicol\'as Bernal, Giovanna Cottin, Basti\'an D\'iaz S\'aez, Manuel L\'opez
https://arxiv.org/abs/2507.07089

Testing frozen-in pNGB dark matter with a long-lived dark Higgs
We consider a simple Higgs portal dark matter (DM) model, where the Standard Model is extended with a complex singlet scalar. The imaginary part of the scalar becomes a massive and stable pseudo-Nambu-Goldstone boson, serving as the DM candidate, while the real part gives rise to a second (dark) Higgs boson. We focus on the freeze-in production of the DM, paying particular attention to low-reheating temperature scenarios, where the dark Higgs can be a long-lived particle (LLP). We also explore …

🇺🇦 Auf radioeins läuft...
Sophia Kennedy:
🎵 Imaginary Friend (Radio Edit)
#NowPlaying #SophiaKennedy
https://sophiakennedy.bandcamp.com/track/imaginary-friend
https://open.spotify.com/track/7CbVZ2Yzl0TtcCERaJDZSR

The imaginary case of the nonabelian Cohen--Lenstra heuristics
Yuan Liu, Ken Willyard
https://arxiv.org/abs/2507.21558 https://arxiv.org/pdf/2507.21558

The imaginary case of the nonabelian Cohen--Lenstra heuristics
For a finite group $Γ$, we study the distribution of the Galois group $G_{\emptyset}^{\#}(K)$ of the maximal unramified extension of $K$ that is split completely at $\infty$ and has degree prime to $|Γ|$ and $\textit{Char}(K)$, as $K$ varies over imaginary $Γ$-extensions of $\mathbb{Q}$ or $\mathbb{F}_q(t)$. In the function field case, we compute the moments of the distribution of $G_{\emptyset}^{\#}(K)$ by counting points on Hurwitz stacks. In order to understand the probability o…

🇺🇦 Auf #radioeins läuft...
Sophia Kennedy:
🎵 Imaginary Friend (Radio Edit)
#NowPlaying #SophiaKennedy
https://sophiakennedy.bandcamp.com/track/imaginary-friend
https://open.spotify.com/track/7CbVZ2Yzl0TtcCERaJDZSR

"If I were in Space": Understanding and Adapting to Social Isolation through Designing Collaborative Narratives
Qi Gong, Ximing Shen, Ziyou Yin, Yaning Li, Ray Lc
https://arxiv.org/abs/2507.15081

"If I were in Space": Understanding and Adapting to Social Isolation through Designing Collaborative Narratives
Social isolation can lead to pervasive health issues like anxiety and loneliness. Previous work focused on physical interventions like exercise and teleconferencing, but overlooked the narrative potential of adaptive strategies. To address this, we designed a collaborative online storytelling experience in social VR, enabling participants in isolation to design an imaginary space journey as a metaphor for quarantine, in order to learn about their isolation adaptation strategies in the process. …

$\mathcal{PT}$-symmetric two-photon quantum Rabi models
Yi-Cheng Wang, Jiong Li, Qing-Hu Chen
https://arxiv.org/abs/2507.20508 https://arxiv.org/pdf/2507.2…

$\mathcal{PT}$-symmetric two-photon quantum Rabi models
We investigate two non-Hermitian two-photon quantum Rabi models (tpQRM) that exhibit $\mathcal{PT}$ symmetry: the biased tpQRM (btpQRM), in which the qubit bias is purely imaginary, and the dissipative tpQRM (dtpQRM), where the two-photon coupling is made imaginary to introduce dissipation. For both models, we derive exact solutions by employing Bogoliubov transformations. In the btpQRM, we identify spectral collapse at a critical coupling strength, with accompanying $\mathcal{PT}$ symmetry bre…

Timelike Entanglement Entropy in Higher Curvature Gravity
Zi-Xuan Zhao, Long Zhao, Song He
https://arxiv.org/abs/2509.04181 https://arxiv.org/pdf/2509.0418…

Timelike Entanglement Entropy in Higher Curvature Gravity
This work investigates holographic timelike entanglement entropy in higher curvature gravity, with a particular focus on Lovelock theories and on the role of excited states. For strip subsystems, higher-curvature terms are found to affect the imaginary part of the entropy in a dimension-dependent manner, while excited states contribute solely to the real part. For the cases analyzed, spacelike and timelike entanglement entropies exhibit proportional relations: vacuum contributions differ by uni…

Quantics Tensor Train for solving Gross-Pitaevskii equation
Aleix Bou-Comas, Marcin P{\l}odzie\'n, Luca Tagliacozzo, Juan Jos\'e Garc\'ia-Ripoll
https://arxiv.org/abs/2507.03134

Quantics Tensor Train for solving Gross-Pitaevskii equation
We present a quantum-inspired solver for the one-dimensional Gross-Pitaevskii equation in the Quantics Tensor-Train (QTT) representation. By evolving the system entirely within a low-rank tensor manifold, the method sidesteps the memory and runtime barriers that limit conventional finite-difference and spectral schemes. Two complementary algorithms are developed: an imaginary-time projector that drives the condensate toward its variational ground state and a rank-adapted fourth-order Runge-Kutt…

A Clarification on Quantum-Metric-Induced Nonlinear Transport
Xiao-Bin Qiang, Tianyu Liu, Zi-Xuan Gao, Hai-Zhou Lu, X. C. Xie
https://arxiv.org/abs/2508.02088 https://

A Clarification on Quantum-Metric-Induced Nonlinear Transport
Over the years, Berry curvature, which is associated with the imaginary part of the quantum geometric tensor, has profoundly impacted many branches of physics. Recently, quantum metric, the real part of the quantum geometric tensor, has been recognized as indispensable in comprehensively characterizing the intrinsic properties of condensed matter systems. The intrinsic second-order nonlinear conductivity induced by the quantum metric has attracted significant recent interest. However, its expre…

Quantum Black Holes: Perihelion Advance, Quasi Normal Modes and Classical/ Topological Thermodynamics
Grigoris Panotopoulos, Francisco Tello-Ortiz
https://arxiv.org/abs/2507.22945

Quantum Black Holes: Perihelion Advance, Quasi Normal Modes and Classical/ Topological Thermodynamics
We report on some properties of a quantum black hole obtained recently. The correction to the Newtonian gravitational potential is proportional to a coupling $α$, which is the only free parameter of the theory. We constrain the coupling using the perihelion advance, we compute the quasi-normal modes for scalar (both massless and massive) and electromagnetic perturbations. We find that all modes computed here are complex numbers characterized by a positive real part and a negative imaginary par…

$p$-adic Higher Green's Functions for Stark-Heegner Cycles
Hazem Hassan
https://arxiv.org/abs/2509.09446 https://arxiv.org/pdf/2509.09446

$p$-adic Higher Green's Functions for Stark-Heegner Cycles
Heegner cycles are higher weight analogues of Heegner points. Their arithmetic intersection numbers also appear as Fourier coefficients of modular forms and often belong to abelian extensions of imaginary-quadratic fields. Rotger and Seveso propose a precise recipe for the $p$-adic Abel-Jacobi images of cycle classes whose existence is predicted by conjectures of Bloch and Beilinson and which would be a real-quadratic analogue to Heegner cycles: the Stark-Heegner cycles of the title. In this …

Quantum Geometry Phenomena in Condensed Matter Systems
Anyuan Gao, Naoto Nagaosa, Ni Ni, Su-Yang Xu
https://arxiv.org/abs/2508.00469 https://arxiv.org/pdf/…

Quantum Geometry Phenomena in Condensed Matter Systems
Quantum geometry, which describes the geometry of Bloch wavefunctions in solids, has become a cornerstone of modern quantum condensed matter physics. The quantum geometrical tensor encodes this geometry through two fundamental components: the quantum metric (real part) and the Berry curvature (imaginary part). While the Berry curvature gained prominence through its manifestation in the intrinsic anomalous Hall effect, recent advances have revealed equally significant effects arising from the qu…

Asymptotic properties of zeros of Riemann zeta function
Juan Arias de Reyna, Yves Meyer
https://arxiv.org/abs/2507.07253 https://arxi…

Asymptotic properties of zeros of Riemann zeta function
We try to define the sequence of zeros of the Riemann zeta function by an intrinsic property. Let $(z_k)_{k\in \mathbb{N}}$ be the sequence of nontrivial zeros of $ζ(s)$ with positive imaginary part. We write $z_k= 1/2+iτ_k$ (RH says that these $τ_k$ are all real). Then the sequence $(τ_k)_{k\in \mathbb{N}},$ satisfies the following asymptotic relation \[\sum_{k\in\mathbb{N}}\frac{2x}{x^2+τ_k^2}\simeq \frac12\log\frac{x}{2π}+\sum_{n=1}^\infty \frac{a_n}{x^n},\,\,x\to +\infty\] where $a_{2…

Primal S-matrix bootstrap with dispersion relations
Claudia de Rham, Andrew J. Tolley, Zhuo-Hui Wang, Shuang-Yong Zhou
https://arxiv.org/abs/2506.22546 htt…

Primal S-matrix bootstrap with dispersion relations
We propose a new method for constructing the consistent space of scattering amplitudes by parameterizing the imaginary parts of partial waves and utilizing dispersion relations, crossing symmetry, and full unitarity. Using this framework, we explicitly compute bounds on the leading couplings and examine the Regge behaviors of the constructed amplitudes. The method also readily accommodates spinning bound states, which we use to constrain glueball couplings. By incorporating dispersion relations…

Enhanced shape recovery in advection--diffusion problems via a novel ADMM-based CCBM optimization
Elmehdi Cherrat, Lekbir Afraites, Julius Fergy Tiongson Rabago
https://arxiv.org/abs/2508.16898

Enhanced shape recovery in advection--diffusion problems via a novel ADMM-based CCBM optimization
This work proposes a novel shape optimization framework for geometric inverse problems governed by the advection-diffusion equation, based on the coupled complex boundary method (CCBM). Building on recent developments [2, 45, 46, 47, 51], we aim to recover the shape of an unknown inclusion via shape optimization driven by a cost functional constructed from the imaginary part of the complex-valued state variable over the entire domain. We rigorously derive the associated shape derivative in vari…

Determination of ground states of one-dimensional quantum systems using the cluster iTEBD method
Tao Yang, Rui Wang, Z. Y. Xie, Baigeng Wang
https://arxiv.org/abs/2508.21405 htt…

Determination of ground states of one-dimensional quantum systems using the cluster iTEBD method
Within the framework of imaginary-time evolution for matrix product states, we introduce a cluster version of the infinite time-evolving block decimation algorithm for simulating quantum many-body systems, addressing the computational accuracy challenges in strongly correlated physics. By redefining the wave-function ansatz to incorporate multiple physical degrees of freedom, we enhance the representation of entanglement, thereby improving the accuracy of the ground states. Utilizing the Trotte…

Optimization by VarQITE on Adaptive Variational Quantum Kolmogorov-Arnold Network
Hikaru Wakaura, Rahmat Mulyawan, Andriyan B. Suksmono
https://arxiv.org/abs/2506.22801

Optimization by VarQITE on Adaptive Variational Quantum Kolmogorov-Arnold Network
Quantum imaginary time evolution (QITE) is a powerful method to derive the ground states of the systems. Only the damping of quantum states leads it; hence, reaching the ground state is guaranteed by nature without any external manipulation. Numerous QITE methods by many groups are used to improve speed and accuracy, derive excited states, and solve combined optimization problems. However, the QITE methods have not been used for quantum machine learning to predict the ideal values for multiple …

Beyond asymptotic reasoning: a practical ground state projector based on the wall-Chebyshev expansion
Maria-Andreea Filip, Nathan Fitzpatrick
https://arxiv.org/abs/2508.00533 ht…

Beyond asymptotic reasoning: a practical ground state projector based on the wall-Chebyshev expansion
We introduce a quantum algorithm for ground-state preparation based on a Chebyshev series approximation to the wall function. This projector can be efficiently implemented as a product of Hamiltonian operators, enabling a straightforward realization via the linear combinations of unitaries method. We analyze the asymptotic scaling and provide numerical benchmarks, demonstrating that the wall-Chebyshev projector achieves competitive performance with leading methods based on imaginary time evolut…

Quark mass dependence of a QCD critical point and structure of the Columbia plot
Julian Bernhardt, Christian S. Fischer
https://arxiv.org/abs/2507.21680 https://

Quark mass dependence of a QCD critical point and structure of the Columbia plot
We study the quark-mass dependence of the QCD critical point at varying bare up/down quark masses with fixed strange quark mass. We explore the corresponding second-order critical surface in the three-dimensional Columbia plot and study the extension of the associated crossover hyperplane at real and imaginary baryon chemical potential. To this end, we employ a by now well-tested combination of lattice Yang--Mills theory and a (truncated) version of Dyson--Schwinger equations at $N_f=2+1$ quark…

Unstable mode and the Unruh-DeWitt detector
Bruno S. Felipe, Jo\~ao P. M. Pitelli
https://arxiv.org/abs/2508.20993 https://arxiv.org/pdf/2508.20993

Unstable mode and the Unruh-DeWitt detector
We investigate the quantization of a single unstable mode in a real scalar field subject to a Robin boundary condition in (1+1)-dimensional half-Minkowski spacetime. The instability arises from an imaginary frequency mode - analogous to that of the inverted harmonic oscillator - requiring the rigged Hilbert space formalism for consistent quantization. Within this framework, the unstable mode is naturally described as a well-defined decaying (or growing) quantum state with a characteristic mean …

Constructions of lattices via biquadratic and triquadratic fields
L. F. Santos, G. C. Jorge
https://arxiv.org/abs/2509.04591 https://arxiv.org/pdf/2509.045…

Constructions of lattices via biquadratic and triquadratic fields
The lattices $D_4$ and $E_8$ are known to be the densest lattices in dimensions 4 and 8, respectively. In this paper, we employ tools from algebraic number theory to prove that the $D_4$-lattice arises from an infinite family of totally imaginary biquadratic fields. Furthermore, we extend this construction to show that both the $D_8$ and $E_8$ can be realized via triquadratic fields derived from this family.

Quadratic Chabauty Experiments on Genus 2 Bielliptic Modular Curves in the LMFDB
Kate Finnerty
https://arxiv.org/abs/2507.03784 https://

Quadratic Chabauty Experiments on Genus 2 Bielliptic Modular Curves in the LMFDB
We present results of quadratic Chabauty experiments on genus 2 bielliptic modular curves of Jacobian rank 2 that have recently been added to the LMFDB. We apply quadratic Chabauty methods over both the rationals and quadratic imaginary fields. In a number of cases, the experiments yielded algebraic irrational points among the set of mock rational points. We highlight specific notable examples, including the non-split Cartan modular curve $X^+_{ns}(15)$. Lastly, we offer a conjecture relating t…

Selberg's Central Limit Theorem weighted by Linear Statistics of Zeta Zeros
Alessandro Fazzari, Maxim Gerspach, Paolo Minelli
https://arxiv.org/abs/2507.04150

Selberg's Central Limit Theorem weighted by Linear Statistics of Zeta Zeros
We consider the value distribution of the logarithm of the Riemann zeta function on the critical line, weighted by the local statistics of zeta zeros. We show that, with appropriate normalization, it satisfies a complex Central Limit Theorem, provided that the Fourier support of the test function in the linear statistics is sufficiently small. For the imaginary part, we extend this support condition up to its natural barrier under the Riemann Hypothesis. Finally, we prove that the correlation b…

Replaced article(s) found for quant-ph. https://arxiv.org/list/quant-ph/new
[2/2]:
- Toward quantum tunneling from excited states: Recovering imaginary-time instantons from a real-ti...
Thomas Steingasser, David I. Kaiser

Farey neighbours, modular symbols and divergent geodesics
Jouni Parkkonen, Fr\'ed\'eric Paulin
https://arxiv.org/abs/2509.02269 https://arxiv.org/p…

Farey neighbours, modular symbols and divergent geodesics
We give effective asymptotic counting results for pairs of Farey neighbours and for modular symbols in $\mathbb Q$, in imaginary quadratic number fields and in definite quaternion algebras over $\mathbb Q$, using the distribution of common perpendiculars between Margulis cusp neighbourhoods and divergent geodesics in hyperbolic manifolds. We describe the tangency properties of the canonical Margulis cusp neighbourhoods in Bianchi hyperbolic $3$-orbifolds.

Complex Heat Capacity as a Witness of Spatio-Temporal Entanglement
Mia Stamatova, Vlatko Vedral
https://arxiv.org/abs/2508.15728 https://arxiv.org/pdf/2508…

Complex Heat Capacity as a Witness of Spatio-Temporal Entanglement
We propose a novel witness of temporal quantum entanglement using the imaginary component of the complex heat capacity - a measurable thermodynamic quantity in temperature-modulated calorimetry. By establishing a direct correspondence between complex heat capacity and the pseudo-density matrix formalism, our approach enables the characterisation of both spatial and temporal quantum correlations without demanding additional state-level manipulation beyond initial tomography. We analytically demo…

Irreducibility of polarized automorphic Galois representations in infinitely many dimensions
Zachary Feng, Dmitri Whitmore
https://arxiv.org/abs/2507.22631 https://

Irreducibility of polarized automorphic Galois representations in infinitely many dimensions
Let \( π\) be a polarized, regular algebraic, cuspidal automorphic representation of \( \GL_n(\bb{A}_F) \) where \( F \) is totally real or imaginary CM, and let \( (ρ_λ)_λ\) be its associated compatible system of Galois representations. We prove that if \( 7\nmid n \) and \( 4 \nmid n \) then there is a Dirichlet density \( 1 \) set of rational primes \( \mc{L} \) such that whenever \( λ\mid \ell \) for some \( \ell\in \mc{L} \), then \( ρ_λ\) is irreducible.

Diagonal cycles and Anticyclotomic twists of modular forms at inert primes
Luca Marannino
https://arxiv.org/abs/2507.22755 https://arxiv.org/pdf/2507.22755…

Diagonal cycles and Anticyclotomic twists of modular forms at inert primes
We revisit the construction of Castella and Do of an anticyclotomic Euler system for the $p$-adic Galois representation of a modular form, using diagonal classes. Combining this construction and some previous results of ours, we obtain new results towards the Bloch--Kato conjecture in analytic rank one, assuming that the fixed prime $p$ is inert in the relevant imaginary quadratic field.

Duality for arithmetic Dijkgraaf-Witten theory
Jaro Eichler
https://arxiv.org/abs/2508.19214 https://arxiv.org/pdf/2508.19214

Duality for arithmetic Dijkgraaf-Witten theory
Naidu classified pairs of finite groups and 3-cocycles that lead to equivalent Dijkgraaf-Witten theories for 3-manifolds. We establish analogous equivalences for arithmetic Dijkgraaf-Witten theory over totally imaginary number fields F containing n-th roots of unity, where n is invertible on X subset spec O_F. For the full ring of integers X = spec O_F, we give examples with quadratic fields and the quaternion group Q_8 where these equivalences fail, but also identify sufficient conditions unde…

Linear independence measures for Chowla--Selberg periods
Wadim Zudilin
https://arxiv.org/abs/2508.17738 https://arxiv.org/pdf/2508.17738

Linear independence measures for Chowla--Selberg periods
We use simultaneous Padé approximations to $_3F_2$ hypergeometric functions to estimate from below linear forms in $1$, $π\sqrt{d}$, $Ω_D/π$ and $π/Ω_D$ with integral coefficients, where $d$ is a positive integer and $Ω_D$ is (the square of) a Chowla--Selberg period attached to the imaginary quadratic field $Q(\sqrt{D})$.