Electrostatic computations for statistical mechanics and random matrix applicationsAlthough for the most part classical, the topic of electrostatics finds to this day new applications. In this review we highlight several theoretical results on electrostatics, chosen to both…Sung-Soo Byun, Peter J. Forrester·Oct 16, 2025SaveLearn
Totally Anti-symmetric Spinor Tensors in Minkowski SpaceThe spinor tensor εAB has a special property that its elements can be formulated into an algebraic expression of the indices. All the totally anti-symmetric tensors in Minkowski space are…Peng Liu, Tanweer Sohail, Xiaoyu Jia·Oct 15, 2025SaveLearn
A Note on Optimal Soft Edge Expansions for the Gaussian β EnsemblesWe present some review material relating to the topic of optimal asymptotic expansions of correlation functions and associated observables for β ensembles in random matrix theory. We also give…Peter J. Forrester, Anas A. Rahman, Bo-Jian Shen·Oct 15, 2025SaveLearn
Detecting screens modeled by Schrödinger operators that generate C0 contraction semigroupsConsider a non-relativistic quantum particle with wave function ψ in a bounded C2 region Ω⊂ Rn, and suppose detectors are placed along the boundary ∂ Ω. Assume the…Lawrence Frolov·Oct 15, 2025SaveLearn
On the Hierarchy of Scales in Modeling of Weakly Interacting Chains of AtomsIn the first part of this paper, we apply a well known discrete-to-continuum approach to a Frenkel-Kontorova-type model of an infinitely long one-dimensional chain of atoms weakly interacting with a…Dmitry Golovaty, J. Patrick Wilber·Oct 14, 2025SaveLearn
Constructing Solutions of Simplex Equations from Polygon EquationsWe study polygon equations and their connections to simplex equations, which generalize the pentagon and Yang-Baxter equations, respectively. First, we show that certain…Serban Matei Mihalache, Tomoro Mochida·Oct 14, 2025SaveLearn
Iterative polynomial regularisation of PIV-type: Hamiltonian systems and Newton polygonsWe study several polynomial Hamiltonian systems of PIV-type (including the mixed case quasi-PIV), and show that via the iterative process of polynomial regularisation, it is possible to identify the…Marta Dell'Atti, Galina Filipuk·Oct 14, 2025SaveLearn
Reduced Density Matrix Functional Theory And A Reduced Formulation Of Density Functional TheoryA mathematical framework for reduced density matrix functional theory (RDMFT) is proposed. The work is inspired by and generalizes the work by E.H.~Lieb [E.H. Lieb, Int. J. Quant. Chem. 24(1983),…Håkon R. Fredheim, Simen Kvaal·Oct 14, 2025SaveLearn
On linear waves with memory in a Bessel-like mediumWe discuss the propagation of harmonic and transient waves for systems governed by a wave equation with memory whose integral kernel involves ratios of modified Bessel functions of the first kind in…A. Giusti, I. Colombaro, A. Mentrelli·Oct 13, 2025SaveLearn
On the construction of Hadamard states from Feynman propagatorsThe Wightman two-point function of any Hadamard state of a linear quantum field theory determines a corresponding Feynman propagator. Conversely, however, a Feynman propagator determines a state only…Christopher J. Fewster, Alexander Strohmaier·Oct 13, 2025SaveLearn
Area Law for the entanglement entropy of free fermions in nonrandom ergodic fieldThis paper deals with the asymptotic behaviour of a widely used correlation characteristic in large quantum systems. The correlations are known as quantum entanglement, the characteristic is called…Leonid Pastur, Mira Shamis·Oct 13, 2025SaveLearn
Superoscillations and the Klein-Gordon equation via the Fourier methodWe investigate the time-evolution problem associated with the Klein-Gordon equation, using superoscillations as initial data. Additionally, the Segal-Bargmann transform is used to derive integral…Kamal Diki, Simon Verbruggen·Oct 12, 2025SaveLearn
A topological counting rule for shellsHolding a shell in their hands, one can apply six loads: three by pulling and shearing, and three by bending and twisting. Here, it is shown that the shell resists exactly three load cases and comply…Hussein Nassar·Oct 12, 2025SaveLearn
Equivalence of quantizations of the dispersionless KdV hierarchyWang recently constructed a quantization of the dispersionless KdV hierarchy using the Heisenberg vertex algebra. Independently, in joint work with Rossi, we obtained a quantization of the…Xavier Blot·Oct 11, 2025SaveLearn
First Passage Problem: Asymptotic Corrections due to Discrete SamplingHow long a stochastic process survives before leaving a domain depends not only on its intrinsic dynamics but also on how it is observed. Classical first-passage theory assumes continuous monitoring…Lars Fritz·Oct 11, 2025SaveLearn
On Riemann wave superpositions obtained from the Euler systemThe paper contains an analysis of the conditions for the existence of elastic versus non-elastic wave superpositions governed by the Euler system in (1+1)-dimensions. A review of recently obtained…Łukasz Chomienia, Alfred Michel Grundland·Oct 10, 2025SaveLearn
Modeling Protein Diffusion Across ER-Nuclear Envelope Junctions Reveals Efficient Transport via Simple DiffusionThe endoplasmic reticulum (ER) is the largest continuous membrane-bound organelle in the cell and plays a central role in the synthesis and turnover of many lipids and proteins. It connects directly…Sara Merino-Aceituno, Carmela Moschella, Shotaro Otsuka et al.·Oct 10, 2025SaveLearn
Operator-Consistent Physics-Informed Learning for Wafer Thermal Reconstruction in LithographyThermal field reconstruction in post-exposure bake (PEB) is critical for advanced lithography, yet current physics-informed neural networks (PINNs) suffer from inconsistent accuracy due to a…Ze Tao, Fujun Liu, Yuxi Jin et al.·Oct 10, 2025SaveLearn
Quantum variance and fluctuations for Walsh-quantized baker's mapsThe Walsh-quantized baker's maps are models for quantum chaos on the torus. We show that for all baker's map scaling factors D2 except for D=4, typically (in the sense of Haar measure on the…Laura Shou·Oct 9, 2025SaveLearn
(Quasi) Hamiltonian Systems and Non-Decomposable Poisson GeometryIn this work, we conduct a systematic study of Hamiltonian and quasi-Hamiltonian systems within the framework of nondecomposable generalized Poisson geometry. Our focus lies on the interplay between…C. Sardón, X. Zhao·Oct 9, 2025SaveLearn
From Dirac to Dunkl Operators through Symmetry ReductionThis paper presents a geometric and analytic derivation of Dirac-Dunkl operators as symmetry reductions of the flat Dirac operator on Euclidean space. Starting from the standard Dirac operator, we…Cristina Sardón·Oct 9, 2025SaveLearn
Open Hurwitz numbers and the mKP hierarchyWe give a natural definition of open Hurwitz numbers, where the weight of each ramified covering includes an integer parameter N taken to the power that is equal to the number of boundary…Alexandr Buryak, Ran J. Tessler, Mikhail Troshkin·Oct 9, 2025SaveLearn
The tensor product of p-adic Hilbert spacesIn the framework of quantum mechanics over a quadratic extension of the ultrametric field of p-adic numbers, we introduce a notion of tensor product of p-adic Hilbert spaces. To this end, following a…Paolo Aniello, Lorenzo Guglielmi, Stefano Mancini et al.·Oct 8, 2025SaveLearn
Quantum Curve for strip geometries, Topological Recursion and open GW/DT invariantsOpen topological string partition function gives rise to open Gromov-Witten invariants, open Donaldson-Thomas invariants and 3D-5D BPS indices. Utilizing the remodelling conjecture which connects…Sibasish Banerjee, Alexander Hock·Oct 8, 2025SaveLearn
Lepage equivalents for second order Lagrangians and applications: 2D modified higher order Boussinesq-type equationsIn the frame of the Lagrangian formalism on r-order prolongations of fibered manifolds and related structures such as (prolongation of) projectable vector fields, (sheaves of) differential forms…Marcella Palese, Fabrizio Zanello·Oct 8, 2025SaveLearn