Tootfinder

Analyzing Black-Hole Ringdowns with Orthonormal Modes
Soichiro Morisaki, Hayato Motohashi, Motoki Suzuki, Daiki Watarai
https://arxiv.org/abs/2507.12376 ht…

Analyzing Black-Hole Ringdowns with Orthonormal Modes
The ringdown signal following a BH merger can be modeled as a superposition of BH QNMs, offering a clean setup for testing gravitational theories. In particular, detecting multiple QNMs enables consistency checks of their frequencies and damping times, serving as a test of General Relativity -- a technique known as black hole spectroscopy. However, incorporating additional QNMs introduces challenges such as increased parameter correlations and higher computational costs in data analysis. To add…

Special vector fields on Riemannian manifolds of constant negative sectional curvature and conservation laws
Keti Tenenblat, Alice Barbora Tumpach
https://arxiv.org/abs/2506.14960

Special vector fields on Riemannian manifolds of constant negative sectional curvature and conservation laws
We show that any $n$-dimensional Riemannian manifold with constant negative sectional curvature admits local orthonormal vector fields such that one of them $v_1$ is tangent to geodesics and the other $n-1$ vector fields are tangent to horocycles. We prove that the $1$-form dual to $v_1$ is a closed form. We show how the closed form can be used to obtain conservation laws for PDEs whose generic solutions define metrics on open subsets with constant negative sectional curvature. These results ex…

A discrete approach to Zhang's projection inequality
David Alonso-Guti\'errez, Eduardo Lucas, Javier Mart\'in Go\~ni
https://arxiv.org/abs/2509.14986 https://…

A discrete approach to Zhang's projection inequality
In this paper we will provide a new proof of the fact that for any convex body $K\subseteq\R^n$ $$ \frac{{{2n}\choose{n}}}{n^n}n\int_0^\infty r^{n-1}\vol_n(K\cap(re_n+K))dr\leq\frac{(\vol_n(K))^{n+1}}{(\vol_{n-1}(P_{e_n^\perp}(K)))^n}, $$ where $(e_i)_{i=1}^n$ denotes the canonical orthonormal basis in $\R^n$, $P_{e_n^\perp}(K)$ denotes the orthogonal projection of $K$ onto the linear hyperplane orthogonal to $e_n$, and $\vol_k$ denotes the $k$-dimensional Lebesgue measure. This inequality was …

Low-degree lower bounds via almost orthonormal bases
Alexandra Carpentier (LMO, CELESTE), Simone Maria Giancola (LMO, CELESTE), Christophe Giraud (LMO, CELESTE), Nicolas Verzelen (MISTEA)
https://arxiv.org/abs/2509.09353

Low-degree lower bounds via almost orthonormal bases
Low-degree polynomials have emerged as a powerful paradigm for providing evidence of statistical--computational gaps across a variety of high-dimensional statistical models [Wein25]. For detection problems -- where the goal is to test a planted distribution $\mathbb{P}'$ against a null distribution $\mathbb{P}$ with independent components -- the standard approach is to bound the advantage using an $\mathbb{L}^2(\mathbb{P})$-orthonormal family of polynomials. However, this method breaks down for…

Mapping continuous-variable quantum states onto optical scalar beams
B. M. Rodr\'iguez-Lara, F. E. Becerra
https://arxiv.org/abs/2509.12426 https://arx…

Mapping continuous-variable quantum states onto optical scalar beams
Optical fields provide an accessible platform to explore connections between classical and quantum mechanics. We introduce a group-theoretic framework based on the $\mathrm{su}(1,1)$ Lie algebra to construct classical analogs of continuous-variable quantum states using the spatial degree of freedom of paraxial scalar beams. Our framework maps squeezed number states onto scalar beams expanded in orthonormal Gaussian modal bases, encompassing both Gaussian and non-Gaussian classical analogs, incl…

Extension of the Jordan-Wigner mapping to nonorthogonal spin orbitals for quantum computing application to valence bond approaches
Alessia Marruzzo, Mos\`e Casalegno, Piero Macchi, Fabio Mascherpa, Bernardino Tirri, Guido Raos, Alessandro Genoni
https://arxiv.org/abs/2509.12680

Extension of the Jordan-Wigner mapping to nonorthogonal spin orbitals for quantum computing application to valence bond approaches
Quantum computing offers a promising platform to address the computational challenges inherent in quantum chemistry, and particularly in valence bond (VB) methods, which are chemically appealing but suffer from high computational cost due to the use of nonorthogonal orbitals. While various fermionic-to-spin mappings exist for orthonormal spin orbitals, such as the widely used Jordan-Wigner transformations, an analogous framework for nonorthogonal spin orbitals remains undeveloped. In this work,…

Maximal estimates for orthonormal systems of wave equations
Shinya Kinoshita, Hyerim Ko, Shobu Shiraki
https://arxiv.org/abs/2508.19446 https://arxiv.org/p…

Maximal estimates for orthonormal systems of wave equations
This paper investigates maximal estimates of the wave operators for orthonormal families of initial data. We extend the classical maximal estimates for the wave operator by making partial progress on maximal estimates for orthonormal systems in low dimensions. Our novel approach is based on a geometric analysis of the kernel of wave operators within the framework of Schatten $2$ estimates. In particular, we exploit Wolff's geometric lemma on the intersection patterns of thickened spheres.

Approximate Sparsity Class and Minimax Estimation
Lucas Z. Zhang
https://arxiv.org/abs/2508.09278 https://arxiv.org/pdf/2508.09278

Approximate Sparsity Class and Minimax Estimation
Motivated by the orthogonal series density estimation in $L^2([0,1],μ)$, in this project we consider a new class of functions that we call the approximate sparsity class. This new class is characterized by the rate of decay of the individual Fourier coefficients for a given orthonormal basis. We establish the $L^2([0,1],μ)$ metric entropy of such class, with which we show the minimax rate of convergence. For the density subset in this class, we propose an adaptive density estimator based on a…

From Product Hilbert Spaces to the Generalized Koopman Operator and the Nonlinear Fundamental Lemma
Mircea Lazar
https://arxiv.org/abs/2508.07494 https://a…

From Product Hilbert Spaces to the Generalized Koopman Operator and the Nonlinear Fundamental Lemma
The generalization of the Koopman operator to systems with control input and the derivation of a nonlinear fundamental lemma are two open problems that play a key role in the development of data-driven control methods for nonlinear systems. Both problems hinge on the construction of observable or basis functions and their corresponding Hilbert space that enable an infinite-dimensional, linear system representation. In this paper we derive a novel solution to these problems based on orthonormal …

Geometry of supergravity and the Batalin--Vilkovisky formulation of the $\mathcal N=1$ theory in ten dimensions
Julian Kupka, Charles Strickland-Constable, Fridrich Valach
https://arxiv.org/abs/2508.06398

Geometry of supergravity and the Batalin--Vilkovisky formulation of the $\mathcal N=1$ theory in ten dimensions
We provide full details of a BV formulation of $\mathcal N=1$ supergravity in ten dimensions, to all orders in fermions, built from the generalised geometry description of the theory. In contrast to standard treatments, we introduce neither the degrees of freedom corresponding to orthonormal frames for the metric nor the local Lorentz symmetries that remove them again. Instead, we observe that the field space has a fibred structure, with the fermionic degrees of freedom spanning the fibres. We …

Quantum Latin squares with all possible cardinalities
Ying Zhang, Xin Wang, Lijun Ji
https://arxiv.org/abs/2507.05642 https://arxiv.o…

Quantum Latin squares with all possible cardinalities
A quantum Latin square of order $n$ (denoted as QLS$(n)$) is an $n\times n$ array whose entries are unit column vectors from the $n$-dimensional Hilbert space $\mathcal{H}_n$, such that each row and column forms an orthonormal basis. Two unit vectors $|u\rangle, |v\rangle\in \mathcal{H}_n$ are regarded as identical if there exists a real number $θ$ such that $|u\rangle=e^{iθ}|v\rangle$; otherwise, they are considered distinct. The cardinality $c$ of a QLS$(n)$ is the numbe…

Towards an Efficient Shifted Cholesky QR for Applications in Model Order Reduction using pyMOR
Maximilian Bindhak, Art J. R. Pelling, Jens Saak
https://arxiv.org/abs/2507.07788

Towards an Efficient Shifted Cholesky QR for Applications in Model Order Reduction using pyMOR
Many model order reduction (MOR) methods rely on the computation of an orthonormal basis of a subspace onto which the large full order model is projected. Numerically, this entails the orthogonalization of a set of vectors. The nature of the MOR process imposes several requirements for the orthogonalization process. Firstly, MOR is oftentimes performed in an adaptive or iterative manner, where the quality of the reduced order model, i.e., the dimension of the reduced subspace, is decided on the…

Efficient streaming dynamic mode decomposition
Aditya Kale, Marcos Netto, Xinyang Zhou
https://arxiv.org/abs/2507.03770 https://arxiv…

Efficient streaming dynamic mode decomposition
We propose a reformulation of the streaming dynamic mode decomposition method that requires maintaining a single orthonormal basis, thereby reducing computational redundancy. The proposed efficient streaming dynamic mode decomposition method results in a constant-factor reduction in computational complexity and memory storage requirements. Numerical experiments on representative canonical dynamical systems show that the enhanced computational efficiency does not compromise the accuracy of the p…

On the cardinalities of quantum Latin squares
Yajuan Zang, Meihui Zheng, Zihong Tian, Xiuling Shan
https://arxiv.org/abs/2508.01972 https://arxiv.org/pdf/2…

On the cardinalities of quantum Latin squares
A quantum Latin square of order $v$, QLS($v$), is a $v\times v$ array in which each of entries is a unit column vector from the Hilbert space $\mathbb{C}^{v}$, such that every row and column forms an orthonormal basis of $\mathbb{C}^{v}$. The cardinality of a QLS($v$) is the number of its vectors distinct up to a global phase, which is the crucial indicator for distinguishing between classical QLSs and non-classical QLSs. In this paper, we investigate the possible cardinalities of a QLS($v$). A…

The Properties of Ces\'aro General Fourier Sums of Functions with Derivatives of Lipschitz Class Functions
G. Tutberidze, V. Tsagareishvili, G. Cagareishvil
https://arxiv.org/abs/2509.07466

The Properties of Cesáro General Fourier Sums of Functions with Derivatives of Lipschitz Class Functions
In this paper, we investigate the Cesáro means of Fourier series with respect to general orthonormal systems (ONS), when the function \( f \) belongs to a certain differentiable class of functions. It is well known that the membership of a function \( f \not\equiv 0 \) in a differentiable class does not, in general, guarantee the summability of its Fourier series with respect to an arbitrary ONS. Therefore, in order for the Fourier series with respect to a given ONS to be summable, one mu…

Equivalence of mutually unbiased bases via orbits: general theory and a $d=4$ case study
Amit Te'eni, Eliahu Cohen
https://arxiv.org/abs/2508.15412 https://

Equivalence of mutually unbiased bases via orbits: general theory and a $d=4$ case study
In quantum mechanics, mutually unbiased bases (MUBs) represent orthonormal bases that are as "far apart" as possible, and their classification reveals rich underlying geometric structure. Given a complex inner product space, we construct the space of its orthonormal bases as a discrete quotient of the complete flag manifold. We introduce a metric on this space, which corresponds to the "MUBness" distance. This allows us to describe equivalence between sets of mutually unbiased bases in terms of…

The Haar State values of monomials and a method to pick orthonormal bases on $O(U_q(3))$
Ting Lu
https://arxiv.org/abs/2508.15346 https://arxiv.org/pdf/250…

The Haar State values of monomials and a method to pick orthonormal bases on $O(U_q(3))$
In this paper, we investigate the evaluation problem of the Haar state on the quantum group $O(U_q(n))$ ($n\ge 3$) which is a $q$-deformation of the Haar measure on the Lie group $U(n)$. The relation between the Haar state values of monomials on $O(U_q(n))$ is studied. On $O(U_q(3))$, the Haar state values of monomials are explicitly computed and these values are expressed as a finite summation of rational polynomials in $q$. As an application, we compute the Gram matrices of the irreducible co…

Maximal estimates for orthonormal systems of wave equations with sharp regularity
Hyerim Ko, Sanghyuk Lee, Shobu Shiraki
https://arxiv.org/abs/2508.19451 https://

Maximal estimates for orthonormal systems of wave equations with sharp regularity
We study maximal estimates for the wave equation with orthonormal initial data. In dimension $d=3$, we establish optimal results with the sharp regularity exponent up to the endpoint. In higher dimensions $d \ge 4$ and also in $d=2$, we obtain sharp bounds for the Schatten exponent (summability index) $β\in [2, \infty]$ when $d\ge4$, and $β\in[1, 2]$ when $d=2$, improving upon the previous estimates due to Kinoshita--Ko--Shiraki. Our approach is based on a novel analysis of a key integral ari…

Quadratic forms of holomorphic cusp forms and the decay of their $\ell^p$-norms for $0 < p < 2$
Shenghao Hua
https://arxiv.org/abs/2507.21951 https://

Quadratic forms of holomorphic cusp forms and the decay of their $\ell^p$-norms for $0 < p < 2$
In this paper, we demonstrate that, given an orthonormal basis of holomorphic Hecke cusp forms, conditionally, quadratic forms composed of cusp forms -- each expressed as a bounded linear combination of holomorphic Hecke cusp forms -- are generally not themselves expressible as bounded linear combinations of holomorphic Hecke cusp forms when the sum of the weights exceeds some absolute constant, provided that the coefficients of the quadratic form satisfy appropriate nonvanishing and boundednes…

Classification of biharmonic Riemannian submersions from manifolds with constant sectional curvature
Shun Maeta, Miho Shito
https://arxiv.org/abs/2509.05939 https://

Classification of biharmonic Riemannian submersions from manifolds with constant sectional curvature
In 2011, Wang and Ou (Math. Z. 269:917-925, 2011) showed that any biharmonic Riemannian submersion from a 3-dimensional Riemannian manifold with constant sectional curvature to a surface is harmonic. In this paper, we generalize the 3-dimensional setting to arbitrary dimensions. By constructing an adapted orthonormal frame, we simplify the biharmonic equation for Riemannian submersions and analyze the curvature properties of Riemannian manifolds with constant sectional curvature. As a result, w…

Learning quadratic neural networks in high dimensions: SGD dynamics and scaling laws
G\'erard Ben Arous, Murat A. Erdogdu, N. Mert Vural, Denny Wu
https://arxiv.org/abs/2508.03688

Learning quadratic neural networks in high dimensions: SGD dynamics and scaling laws
We study the optimization and sample complexity of gradient-based training of a two-layer neural network with quadratic activation function in the high-dimensional regime, where the data is generated as $y \propto \sum_{j=1}^{r}λ_j σ\left(\langle \boldsymbol{θ_j}, \boldsymbol{x}\rangle\right), \boldsymbol{x} \sim N(0,\boldsymbol{I}_d)$, $σ$ is the 2nd Hermite polynomial, and $\lbrace\boldsymbolθ_j \rbrace_{j=1}^{r} \subset \mathbb{R}^d$ are orthonormal signal directions. We consider the ex…

Strichartz estimates involving orthonormal systems at the critical summability exponent
Guoxia Feng, Manli Song, Huoxiong Wu
https://arxiv.org/abs/2507.14974

Strichartz estimates involving orthonormal systems at the critical summability exponent
The primary objective of this paper is to investigate the orthonormal Strichartz estimates at the critical summability exponent for the Schrödinger operator $e^{itΔ}$ with initial data from the homogeneous Sobolev space $\dot{H}^s (\mathbb{R}^n)$. We prove new global strong-type orthonormal Strichartz estimates in the interior of $ODCA$ at the optimal summability exponent $α=q$, thereby substantially supplymenting the work of Bez-Hong-Lee-Nakamura-Sawano \cite{Bez-Hong-Lee-Nakamura-Sawano}. …

Symmetric Localizable Multipartite Quantum Measurements from Pauli Orbits
Jef Pauwels, Cyril Branciard, Alejandro Pozas-Kerstjens, Nicolas Gisin
https://arxiv.org/abs/2509.01851

Symmetric Localizable Multipartite Quantum Measurements from Pauli Orbits
While the structure of entangled quantum states is relatively well understood, the characterization of entangled measurements, especially in multipartite and high-dimensional settings, remains far less developed. In this work, we introduce a general approach to construct highly symmetric, locally encodable orthonormal measurement bases, as orbits of a single fiducial state under tensor-product actions of Pauli subgroups. This framework recovers the Elegant Joint Measurement-a two-qubit measurem…

H-Toeplitz operators on Fock space
Thokchom Sonamani Singh, M. Premjit Singh, Oinam Nilbir Singh, Khumballambam Priyobarta Singh
https://arxiv.org/abs/2507.06532

H-Toeplitz operators on Fock space
This paper explores H-Toeplitz operators on the Fock space, unifying aspects of Toeplitz and Hankel operators while introducing novel structural properties. We derive explicit matrix representations for these operators with respect to the orthonormal basis of monomials, analyze their commutativity, and establish compactness criteria. Key results include the characterization of commuting H-Toeplitz operators with harmonic symbols and the proof that non-zero H-Toeplitz operators cannot be Hilbert…

Zernike polynomials from the tridiagonalization of the radial harmonic oscillator in displaced Fock states
Hashim A. Yamani, Zouha\"ir Mouayn
https://arxiv.org/abs/2506.22933

Zernike polynomials from the tridiagonalization of the radial harmonic oscillator in displaced Fock states
We revisit the J-matrix method for the one dimensional radial harmonic oscillator (RHO) and construct its tridiagonal matrix representation within an orthonormal basis phi(z)n of L2 (R+);parametrized by a fixed z in the complex unit disc D and n = 0,1,2,.... Remarkably, for fixed n,and varying z in D, the system phi(z)n forms a family of Perelomov-type coherent states associated with the RHO. For each fixed n, the expansion of phi(z)n over the basis (fs) of eigenfunctions of the RHO yields coef…

Global strong solutions to the frame hydrodynamics for biaxial nematic phases
Minjiang Feng, Sirui Li, Qi Zeng
https://arxiv.org/abs/2508.06376 https://arx…

Global strong solutions to the frame hydrodynamics for biaxial nematic phases
In this article, we consider the frame hydrodynamics of biaxial nematic phases, a coupled system between the evolution of the orthonormal frame and the Navier--Stokes equation, which is derived from a molecular-theory-based dynamical tensor model about two second-order tensors. In two and three dimensions, we establish global well-posedness of strong solutions to the Cauchy problem of frame hydrodynamics for small initial data. The key ingredient of the proof relies on estimates of nonlinear te…

Teleparallel gravity from the principal bundle viewpoint
Sebastian Brezina, Eugenia Boffo, Martin Kr\v{s}\v{s}\'ak
https://arxiv.org/abs/2507.23672 https://

Teleparallel gravity from the principal bundle viewpoint
We examine whether the Teleparallel Equivalent of General Relativity (TEGR) can be formulated as a gauge theory in the language of connections on principal bundles. We argue in favor of using either the affine bundle with the Poincaré group or, equivalently, the orthonormal frame bundle with the Lorentz group as the structure group. Following the framework of Trautman--where gauge symmetries are determined using the absolute elements--we set to identify the absolute elements and gauge symmetri…

Orthonormal Strichartz estimates on torus and waveguide manifold and applications
Divyang G. Bhimani, Subhash. R. Choudhary
https://arxiv.org/abs/2507.16712

Orthonormal Strichartz estimates on torus and waveguide manifold and applications
We establish orthonormal Strichartz estimates for the fractional Schrödinger equations on torus and waveguide manifold. In the process, we also improve $\ell^2$ decoupling inequality and establish classical fractional Strichartz estimates on waveguide manifold. This maybe of independent interest. As an application, we establish local well-posednes for the Hartree equations with infinitely many particles with non-trace class initial data.

Curvilinear coordinates and curvature in radiative transport
Johannes Krotz, Ryan G. McClarren
https://arxiv.org/abs/2508.20852 https://arxiv.org/pdf/2508.…

Curvilinear coordinates and curvature in radiative transport
We derive a general expression for the streaming term in radiative transport equa- tions and other transport problems when formulated in curvilinear coordinates, emphasizing coordinate systems adapted to the geometry of the domain and the directional dependence of particle transport. By parametrizing the angular vari- able using a local orthonormal frame, we express directional derivatives in terms of curvature-related quantities that reflect the geometry of underlying spatial man- ifolds. Our …

On the Effective Non-vanishing of Hecke--Maass $L$-functions at Special Points
Zhi Qi
https://arxiv.org/abs/2507.14566 https://arxiv.…

On the Effective Non-vanishing of Hecke--Maass $L$-functions at Special Points
In this paper, we consider the non-vanishing problem for the family of special Hecke--Maass $L$-values $ L (1/2+it_f, f) $ with $f (z)$ in an orthonormal basis of (even or odd) Hecke--Maass cusp forms of Laplace eigenvalue $1/4 + t_f^2$ ($t_f > 0$). We prove that 33% of $L (1/2+it_f, f)$ for $ t_f \leqslant T$ do not vanish as $T \rightarrow \infty$. For comparison, it is known that the non-vanishing proportion is at least 25% for the central $L$-values $L (1/2, f)$. Further, 33% may be raised …

Sectional Curvature, Isotropic Curvature, and Yau's Pinching Problem
Xiaolong Li
https://arxiv.org/abs/2508.21661 https://arxiv.org/pdf/2508.21661

Sectional Curvature, Isotropic Curvature, and Yau's Pinching Problem
We prove that if a closed Riemannian manifold $(M^n,g)$ has finite fundamental group and satisfies the curvature condition \begin{equation*} R_{1313} +R_{1414} +R_{2323} + R_{2424} > \tfrac{1}{2}\left(R_{1212} + R_{3434}\right) \end{equation*} for all orthonormal four-frame $\{e_1, e_2, e_3, e_4\} \subset T_pM$, then $M$ is homeomorphic to a spherical space form. This generalizes the famous sphere theorem under the stronger condition of $\frac{1}{4}$-pinched sectional curvature. As an applica…

Crosslisted article(s) found for math.CA. https://arxiv.org/list/math.CA/new
[1/1]:
- Maximal estimates for orthonormal systems of wave equations
Shinya Kinoshita, Hyerim Ko, Shobu Shiraki

Simulation of silicon ridge waveguide enhanced two-photon absorption from femtosecond pulses
Cael Warner, Ruoheng Zhang
https://arxiv.org/abs/2506.18098 ht…

Simulation of silicon ridge waveguide enhanced two-photon absorption from femtosecond pulses
Field enhancement of two-photon absorption from a 50-fs pulse on a silicon ridge waveguide is simulated for a varying energy downward propagating 800+/-9.42 nm wavelength plane-wave orthonormal to a waveguide in 2D FDTD using ANSYS Lumerical FDTD. Energy absorbed by the waveguide is enhanced due to mode confinement within the standard 500 nm width, 130 nm height silicon ridge waveguide on 90 nm thick silicon and 3 μm silicon dioxide insulator.

Generalized Multiple Operator Integrals and Perturbation Theory for Operators with Continuous Spectra
Shih-Yu Chang
https://arxiv.org/abs/2507.23049 https://

Generalized Multiple Operator Integrals and Perturbation Theory for Operators with Continuous Spectra
Operators with continuous spectra naturally arise in spectral theory, quantum mechanics, automorphic forms, and noncommutative geometry. However, analyzing such operators, particularly in the non-selfadjoint setting, remains challenging due to spectral instability and the lack of an orthonormal basis. This work advances the theory of Multiple Operator Integrals (MOIs) by developing a unified framework for generalized MOIs (GMOIs) associated with general (non-normal, non-selfadjoint) operators p…

p-adic Ghobber-Jaming Uncertainty Principle
K. Mahesh Krishna
https://arxiv.org/abs/2506.18913 https://arxiv.org/pdf/2506.18913

p-adic Ghobber-Jaming Uncertainty Principle
Let $\{τ_j\}_{j=1}^n$ and $\{ω_k\}_{k=1}^n$ be two orthonormal bases for a finite dimensional p-adic Hilbert space $\mathcal{X}$. Let $M,N\subseteq \{1, \dots, n\}$ be such that \begin{align*} \displaystyle \max_{j \in M, k \in N}|\langle τ_j, ω_k \rangle|<1, \end{align*} where $o(M)$ is the cardinality of $M$. Then for all $x \in \mathcal{X}$, we show that \begin{align} (1) \quad \quad \quad \quad \|x\|\leq \left(\frac{1}{1-\displaystyle \max_{j \in M, k \in N}|\la…