Superintegrability of a resonant ghostly tri-Hamiltonian model: polynomial first integrals and transcendental completionWe study classical and quantum superintegrability of a resonant three-dimensional Hamiltonian with indefinite kinetic energy and three Poisson descriptions of the same flow. Besides three commuting…Andreas Fring, Ian Marquette·Oct 1, 2026SaveLearn
Quadratic symmetry algebras and Sturm algebraization of superintegrable systems with magnetic fieldsWe study two three-dimensional quantum superintegrable systems in nonvanishing axially symmetric magnetic fields. For each model the integrals generate a quadratic algebra with a Casimir, and…Shams Ara, Md Fazlul Hoque, Ian Marquette·Oct 1, 2026SaveLearn
Quantum hierarchies of the ILW and BO equations and the DR cycles on the moduli spaces of curvesIn an earlier paper of P. Rossi and the first author, a construction of a wide class of quantum hierarchies was presented, with the input data given by an arbitrary cohomological field theory. A…Alexandr Buryak, Abner Hernandez Rodriguez·Oct 1, 2026SaveLearn
The Buchholz Algebra from the Universal Resolvent Algebra--Particle Structure, Gibbs States, and Closed-Path Expansions without Fock RepresentationsWe construct the Buchholz algebra without a Fock representation, as the bounded inverse limit of intrinsic particle-cutoff quotients of the gauge-fixed resolvent algebra, with isometric…Yoshitsugu Sekine·Oct 1, 2026SaveLearn
On spectrum of the harmonic Kronig-Penney modelWe study the spectral properties of the harmonic modification of the quantum mechanical Kronig-Penney model motivated by the theory of the dressing chain. In particular, we show that in the special…J. Gibbons, A. P. Veselov·Oct 1, 2026SaveLearn
Complete Factorial Asymptotics and Integrable Structure of Generalized Charlier Recurrence CoefficientsWe study the monic recurrence coefficients of the generalized Charlier polynomials associated with the discrete weight \[ ρμ(k) = μk(k!)2, k∈ N0, μ>0. \] We…Mahouton Norbert Hounkonnou·Sep 30, 2026SaveLearn
Discrete differential-geometric Poisson brackets: general theory and explicit constructionsWe review the discrete theory of differential-geometric Poisson brackets as introduced by B. A. Dubrovin, and we present a complete proof of their characterisation in the non-degenerate case. We use…Marta Dell'Atti, Giorgio Gubbiotti, Pierandrea Vergallo·Sep 30, 2026SaveLearn
Cluster Attention Neural Operators for Solving Parametric Partial Differential EquationsTraditional simulations of parametric partial differential equations (PDEs) rely on repetitive computations for each parameter, which makes high-fidelity design impractical. Neural operators address…Ming Zhong, Antonio Colanera, Gianluigi Rozza et al.·Sep 30, 2026SaveLearn
Reconsidering the Vacuum Energy of a Massive Scalar Field in a Spherical CavityWe reconsider the vacuum (Casimir) energy of a massive scalar field obeying Dirichlet boundary conditions inside a spherical cavity. Using zeta-function regularization, we carefully recalculate the…M. Bordag, I. G. Pirozhenko·Sep 30, 2026SaveLearn
Many-body localization: an introduction for mathematiciansThese notes are based on a mini-course delivered at the Les Houches Summer School, Quantum Theory on All Scales, in August 2026. They introduce many-body localization to mathematicians, emphasizing…Francois Huveneers·Sep 30, 2026SaveLearn
Exact Chained-Word Threshold and Monotone-Path Structure in the Even Root-of-Unity Kaleidoscope Yang-Baxter AlgebraThe Kaleidoscope Yang-Baxter equation of Qiu, Guan, and Yu (2026) is the consistency condition of multiple scattering in Gaudin's kaleidoscope models. At an even order N it involves two…Qihang Wang, Zhiyuan Yao·Sep 30, 2026SaveLearn
Analysis of Delay Differential Equations Using the Offset Linear Canonical TransformMotivated by the work of Ohira and the advantages of the offset linear canonical transform (OLCT) over the Fourier transform (FT), this paper proposes an OLCT based framework for solving a class of…Gita Rani Mahato, Manab Kundu·Sep 30, 2026SaveLearn
Reachable sets under Kolmogorov dynamics in the probability simplexThe finite-time reachability problem - whether two probability vectors can be transformed in a time t through a generator from a given set - is a key question in Markovian dynamics. We address this…Alfonso Fernández de Bobadilla, Mykhailo Hontarenko, Guillem Müller-Rigat et al.·Sep 29, 2026SaveLearn
On the Spectrum of Some Temperley-Lieb Spin ChainsWe review mathematical results about the spectrum of spin-s chains with a nearest neighbor interaction given by the projection onto the singlet state of two spin-s degrees of freedom. Up to…Robert Ferydouni, Bruno Nachtergaele·Sep 29, 2026SaveLearn
Quantum percolation conjecture on regular treesFor Bernoulli bond percolation on every regular tree of degree at least three, we prove that infinite clusters appear strictly before absolutely continuous spectrum. Throughout an explicit…Simon Becker, Izak Oltman·Sep 29, 2026SaveLearn
Continuum Limit for One-Dimensional Moiré RelaxationWe establish convergence of minimizers for a minimal one dimensional atomic-scale model for relaxation in moiré materials to those of a one-dimensional continuum limit functional analogous to those…Hao Lan, Michael Hott, Jeff Calder et al.·Sep 29, 2026SaveLearn
Breaking the Spin Degeneracy for Distributions of Off-Diagonal Scattering Matrix Elements in the Case of Symplectic SymmetryRecently derived exact expressions for the distributions of scattering matrix elements show that all combinations of ingoing and outgoing spin orientations are equally distributed. We propose a model…Nils Gluth, Thomas Guhr·Sep 29, 2026SaveLearn
Influence of Time Reversal Invariance Breaking on the Distribution of Off-Diagonal Scattering Matrix Elements and Cross SectionsScattering theory is a key tool for the investigation of quantum systems. Universal approaches are of interest, particularly in the framework of Random Matrix Theory. Dyson's Threefold way…Nils Gluth, Ahmed Aldabag, Thomas Guhr·Sep 29, 2026SaveLearn
Distribution of Scattering Matrix Elements in the case of Symplectic SymmetryScattering theory is at the core of gaining information about most quantum systems. In general, analytic progress is difficult and the investigation of universal features using statistical methods is…Nils Gluth, Thomas Guhr·Sep 29, 2026SaveLearn
A posteriori controllability of non-linear remodelling in linear elastic continuaWe investigate the a posteriori controllability of remodelling within the framework of Geometric Control Theory applied to continuum systems. Remodelling is described through an isochoric…Salvatore Di Stefano, Marta Zoppello·Sep 29, 2026SaveLearn
Tripartite System Dynamics of Cooperation Ecological Resources and Adaptive RegulationTo address commons dilemmas under costly social cooperation, this paper develops a tripartite coevolutionary system that integrates social behavior, ecological resource dynamics, and institutional…Linjie Liu, Yike Li, Shijia Hua·Sep 29, 2026SaveLearn
Exact Elastodynamic Homogenization of Laminated Composites RevisitedThis paper revisits Willis' elastodynamic homogenization (Mechanics of Materials, 41 (2009) 385-393) of periodic laminate composites and uses the equivalent inclusion-based method (EIM) to…Chunlin Wu, Huiming Yin·Sep 29, 2026SaveLearn
Reduced Solutions of Toda Systems for Arbitrary Complex Simple Lie AlgebrasWe study reduced solutions of Toda systems generated by spherical metrics for an arbitrary complex simple Lie algebra. The main result is an intrinsic centralizer parametrization: for a spherical…Yiqian Shi, Chunhui Wei, Bin Xu·Sep 29, 2026SaveLearn
Integer Sampling and the Identifiability of Mellin ResiduesI prove that all Mellin residues are determined exactly by integer samples known up to errors smaller than every algebraic order, for an explicit class of functions consisting of a slow component…Yifan He·Sep 28, 2026SaveLearn
Combinatorics and loop equations for antisymmetrised and Hermitised matrix product ensemblesThe order m antisymmetrised matrix product ensemble is represented by the product X1T·s XmTJXm·s X1, where X1,…,Xm are independent real Ginibre matrices and J is the…Stephane Dartois, Anas. A Rahman·Sep 28, 2026SaveLearn