Tootfinder

Adjoint ferromagnets
Joaqu\'in L\'opez-Su\'arez, Alexios P. Polychronakos, Konstantinos Sfetsos
https://arxiv.org/abs/2510.11776 https://arxiv.…

Adjoint ferromagnets
We derive the phase structure and thermodynamics of ferromagnets consisting of elementary magnets carrying the adjoint representation of $SU(N)$ and coupled through two-body quadratic interactions. Such systems have a continuous $SU(N)$ symmetry as well as a discrete conjugation symmetry. We uncover a rich spectrum of phases and transitions, involving a paramagnetic and two distinct ferromagnetic phases that can coexist as stable and metastable states in different combinations over a range of t…

Unser zweierlei Maß bei #Enteignung:
Super böse, wenn damit sichere Radwege gebaut werden. Privateigentum ist dann ein hohes Gut.
Super toll, wenn man damit auf der grünen Wiese Neubaugebiete erschließen will.
Im Ort Rastorf beschließt der Rat aus zwei lokalen Listen und CDU einstimmig bei einer Enthaltung ein Enteignungsverfahren, um ein Neubaugebiet zu erschließen, obwohl di…

Enteignung in Rastorf? „Selbst wenn ich 80.000 Euro bekäme, ich wäre nicht käuflich“
Silke Wilde soll ihr Grundstück verkaufen. Die Rastorferin besitzt 267 Quadratmeter auf dem Düsternbrook, über den die Gemeinde ein Baugebiet erschließen möchte. Doch Silke Wilde wehrt sich wie eine Löwin – auch gegen eine mögliche Enteignung.

A time-space B-spline integrator for the Burgers' equation
Idris Dag, Serkan U\u{g}urluo\u{g}lu, Nihat Adar
https://arxiv.org/abs/2510.09408 https://ar…

A time-space B-spline integrator for the Burgers' equation
The purpose of this paper is to propose a new algorithm for obtaining approximate solutions to the Burgers' equation (BE). Integration in time by a quadratic B-spline collocation method is shown. To the best of our knowledge, B-splines have not previously been used to integrate partial differential equations in both time and space. First, the BE is integrated using quadratic B-spline functions in time, and then the time-integrated BE is further solved in space via the cubic B-spline collocation…

Data-Driven Discrete Geofence Design Using Binary Quadratic Programming
Keisuke Otaki, Akihisa Okada, Tadayoshi Matsumori, Hiroaki Yoshida
https://arxiv.org/abs/2509.24679 https…

Data-Driven Discrete Geofence Design Using Binary Quadratic Programming
Geofences have attracted significant attention in the design of spatial and virtual regions for managing and engaging spatiotemporal events. By using geofences to monitor human activity across their boundaries, content providers can create spatially triggered events that include notifications about points of interest within a geofence by pushing spatial information to the devices of users. Traditionally, geofences were hand-crafted by providers. In addition to the hand-crafted approach, recent …

Quantum Krylov Algorithm for Szeg\"o Quadrature
William Kirby, Yizhi Shen, Daan Camps, Anirban Chowdhury, Katherine Klymko, Roel Van Beeumen
https://arxiv.org/abs/2509.19195

Quantum Krylov Algorithm for Szegö Quadrature
We present a quantum algorithm to evaluate matrix elements of functions of unitary operators. The method is based on calculating quadrature nodes and weights using data collected from a quantum processor. Given a unitary $U$ and quantum states $|ψ_0\rangle$, $|ψ_1\rangle$, the resulting quadrature rules form a functional that can then be used to classically approximate $\langleψ_1|f(U)|ψ_0\rangle$ for any function $f$. In particular, the algorithm calculates Szegö quadr…

On compatible linear and quadratic Poisson brackets on $gl(N)$
Andriy Panasyuk, Taras Skrypnyk
https://arxiv.org/abs/2509.24054 https://arxiv.org/pdf/2509.…

On compatible linear and quadratic Poisson brackets on $gl(N)$
In the present paper, using two constant tensors $c$ and $b$ on $sl(N)\otimes sl(N)$ satisfying certain linear-quadratic equation and a technique of Poisson bivectors and Schouten brackets, we explicitly construct quadratic Poisson bracket on the space $ (sl(N)+\mathbb{C})^*$ which is compatible with the standard Lie--Poisson bracket on $gl(N)^* \simeq (sl(N)\oplus \mathbb{C})^*$. The case of $N=3$ is considered in details. The relation of the proposed brackets with the generalized classical Sk…

Scaling Laws and Spectra of Shallow Neural Networks in the Feature Learning Regime
Leonardo Defilippis, Yizhou Xu, Julius Girardin, Emanuele Troiani, Vittorio Erba, Lenka Zdeborov\'a, Bruno Loureiro, Florent Krzakala
https://arxiv.org/abs/2509.24882

Scaling Laws and Spectra of Shallow Neural Networks in the Feature Learning Regime
Neural scaling laws underlie many of the recent advances in deep learning, yet their theoretical understanding remains largely confined to linear models. In this work, we present a systematic analysis of scaling laws for quadratic and diagonal neural networks in the feature learning regime. Leveraging connections with matrix compressed sensing and LASSO, we derive a detailed phase diagram for the scaling exponents of the excess risk as a function of sample complexity and weight decay. This anal…

Rationality fields of CM modular forms
Kimball Martin
https://arxiv.org/abs/2509.24119 https://arxiv.org/pdf/2509.24119

Rationality fields of CM modular forms
We formulate a conjecture on the finitude of rationality fields (i.e., Fourier coefficient fields) of newforms of bounded degree, and prove this for CM forms assuming a generalized Riemann hypothesis. Then we explicitly determine what quadratic and cubic rationality fields occur for weight 2 CM forms, which is related to classifications of CM abelian varieties of GL(2) type. Several of these fields do not appear in the existing tables of newforms in the LMFDB.

Constructing Jacobians of rank 1
Peter Koymans, Adam Morgan
https://arxiv.org/abs/2509.24937 https://arxiv.org/pdf/2509.24937

Constructing Jacobians of rank 1
Let $K$ be a number field, let $g \geq 1$ be an integer and let $f(x) = (x - a_1) \cdots (x - a_{2g + 1}) \in O_K[x]$ be a polynomial that splits into $2g + 1$ distinct linear factors. Write $C$ for the hyperelliptic curve given by $C: y^2 = f(x)$ and write $J = \mathrm{Jac}(C)$ for its Jacobian. Under mild technical assumptions on $f$ that are satisfied almost always, we prove that there exists some $d \in K^\times$ such that the quadratic twist $J^d$ has rank exactly equal to $1$. As a conseq…

Smearing of dynamical quantum phase transitions in dissipative free-fermion systems
Gilles Parez, Vincenzo Alba
https://arxiv.org/abs/2509.21585 https://ar…

Smearing of dynamical quantum phase transitions in dissipative free-fermion systems
We investigate the Lindblad dynamics of the reduced Loschmidt echo (RLE) in dissipative quadratic fermion systems. Focusing on the case of gain and loss dissipation, we derive general conditions for the persistence of nonanalyticities (so-called dynamical quantum phase transitions) in the time evolution of the RLE. We show that nonanalyticities that are present in the corresponding unitary dynamics can survive under purely gain or purely loss processes, but are completely smeared out as soon as…