Triangular isomonodromic solutions to a Fuchsian system from superelliptic curvesWe give fundamental solutions of arbitrarily sized matrix Fuchsian linear systems, in the case where the coefficients B(i) of the systems are matrix solutions of the Schlesinger system that are…Anwar Al Ghabra, Benjamin Piché, Vasilisa Shramchenko·Jul 14, 2025SaveLearn
N -N duality of SU(N) for stable sequences of representationsWe generalize N -N duality of dimension formulae of SU(N) representations on a (class of) representations with N-dependent Young diagrams (which include the adjoint…R. L. Mkrtchyan·Jul 14, 2025SaveLearn
Distributions of consecutive level spacings of circular unitary ensemble and their ratio: finite-size corrections and Riemann ζ zerosWe compute the joint distribution of two consecutive eigenphase spacings and their ratio for Haar-distributed U(N) matrices (the circular unitary ensemble) using our framework for…Shinsuke M. Nishigaki·Jul 14, 2025SaveLearn
Decomposition and characterization of curl forces for all space dimensionsThis paper introduces a PDE-free algorithmic framework for the local decomposition of classical forces in arbitrary dimensions. By representing a force field as a differential 1-form (work form),…Radosław Antoni Kycia·Jul 13, 2025SaveLearn
Construction of Currents in Causal Fermion SystemsThis paper presents a novel and systematic formalism for deriving classical field equations within the framework ofcausal fermion systems, explicitly accounting for higher-order corrections such as…Felix Finster, Patrick Fischer·Jul 13, 2025SaveLearn
Construction of maximally non-Hermitian potentials under unbroken PT-symmetry constraintA family of discrete Schr\"odinger equations with imaginary potentials V(x) is studied. Inside the domain D of unitarity-compatible values of V(x), the reality of all of the…Miloslav Znojil·Jul 13, 2025SaveLearn
Asymptotics for the noncommutative Painlev\'e II equationIn this paper, we are concerned with the following noncommutative Painlev\'e II equation equation* D2 β1 = 4s β1 +4 β1 s +8 β13,…Junwen Liu, Luming Yao, Lun Zhang·Jul 13, 2025SaveLearn
Feynman Graph Integrals on Kähler ManifoldsIn this paper, we establish the convergence of Feynman graph integrals on closed real-analytic Kähler manifolds and uncover the structural mechanism underlying this convergence. The key insight is…Minghao Wang, Junrong Yan·Jul 12, 2025SaveLearn
A modified Fermi Golden Rule at threshold for 3D magnetic Schr\"odinger operatorsIn this paper we consider three-dimensional Schr\"odinger operators with a simple threshold eigenvalue. We show, under certain assumptions, that when a small magnetic field is introduced, this…Pavel Exner, Arne Jensen, Hynek Kovarik·Jul 12, 2025SaveLearn
A General, Automated Method for Building Structural Tensors of Arbitrary Order for Anisotropic Function RepresentationsWe present a general, constructive procedure to find the basis for tensors of arbitrary order subject to linear constraints by transforming the problem to that of finding the nullspace of a linear…Ravi G. Patel, Reese E. Jones, D. Thomas Seidl et al.·Jul 12, 2025SaveLearn
Free phases of Majorana fermions: Tenfold ways comparedWe provide a mathematically rigorous classification of symmetry-protected topological (SPT) phases of neutral free fermions. Our approach utilizes Karoubi triples with negative squares, thought of as…Luuk Stehouwer·Jul 11, 2025SaveLearn
Shape and Spectrum: On the Heat and Volume of Self-Similar FractalsIn this work, we examine the relationship between geometry and spectrum of regions with fractal boundary. The relationship is well-understood for fractal harps in one dimension, but largely open for…William Hoffer·Jul 11, 2025SaveLearn
Reshetikhin-Turaev construction and U(1)n Chern-Simons partition functionIn this article, we show that the U(1)n Chern-Simons partition functions are related to Reshetikhin-Turaev invariants. In this abelian context, it turns out that the Reshetikhin-Turaev…Michail Tagaris, Frank Thuillier·Jul 11, 2025SaveLearn
Supersymmetry Breaking in Graph Quantum MechanicsIn this paper, we develop the groundwork for a graph theoretic toy model of supersymmetric quantum mechanics. Using discrete Witten-Morse theory, we demonstrate that finite graphs have a natural…Bek Herz, Ivan Contreras·Jul 10, 2025SaveLearn
Koba-Nielsen local zeta functions, convex subsets, and generalized Selberg-Mehta-Macdonald and Dotsenko-Fateev-like integralsThe Koba-Nielsen local zeta functions are integrals depending on several complex parameters, used to regularize the Koba-Nielsen string amplitudes. These integrals are convergent and admit…Willem Veys, W. A. Zúñiga-Galindo·Jul 10, 2025SaveLearn
The rank two Jacobi algebraThe quadratic rank two Jacobi algebra is identified from the relations obeyed by the bispectral operators of the two variable Jacobi polynomials orthogonal on the triangle. It is seen to admit as…Nicolas Crampe, Satoshi Tsujimoto, Luc Vinet et al.·Jul 10, 2025SaveLearn
Group structure as a foundation for entropiesEntropy can signify different things: For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced and it can be difficult to…Henrik Jeldtoft Jensen, Piergiulio Tempesta·Jul 9, 2025SaveLearn
A Twisted sl2(C) Isomonodromic-Isospectral CorrespondenceThe aim of this article is to generalize the isomonodromic-isospectral correspondence for meromorphic connections of rank 2 over P1 to the twisted case. More specifically, the…Mohamad Alameddine·Jul 9, 2025SaveLearn
Linear and Regular Kepler-Manev Dynamics via Projective Transformations: A Geometric PerspectiveThis work presents a geometric formulation for transforming nonconservative mechanical Hamiltonian systems and introduces a new method for regularizing and linearizing central force dynamics -- in…Joseph T. A. Peterson, Manoranjan Majji, John L. Junkins·Jul 9, 2025SaveLearn
Invariant measures on the transversal hull of cone semigroups and some applicationsLet v⊂ D be a suitable cone semigroup and v its reduced semigroup C*-algebra. In this paper, we compute the v-invariant measures in the transversal hull…Danilo Polo Ojito, Emil Prodan, Tom Stoiber·Jul 9, 2025SaveLearn
Exactly solvable inhomogeneous XY spin chainAnalytical expressions for the eigenvalues of certain inhomogeneous XY spin chains are computed. These models are rewritten in terms of free-fermion models using a well-known Jordan-Wigner…Pierre-Antoine Bernard, Nicolas Crampé, Quentin Labriet et al.·Jul 8, 2025SaveLearn
An explanation of the number or points and symmetries of starburstsStarbursts are the light intensity patterns seen when small bright sources are looked at night, typically stars. Starburst shapes are produced when the presence of the eye's wave aberrations…Sergio Barbero, Antonia M. Delgado, Lidia Fernández·Jul 8, 2025SaveLearn
A Homothetic Gauge Theory and the Regularization of the Point ChargeWe introduce a Homothetic Hodge de Rham (HHDR) theory that extends the de Rham complex and Hodge decomposition to homothetically dressed differential forms. The dressing, governed by a dilaton field…Fereidoun Sabetghadam·Jul 8, 2025SaveLearn
Moduli space of spin connections on three-dimensional homogeneous spacesIn this manuscript, we aim to classify and characterize the moduli space of homogeneous spin connections and homogeneous SU(2) connections on three-dimensional Riemannian homogeneous spaces. An…Matteo Bruno, Gabriele Peluso·Jul 8, 2025SaveLearn
BV Pushforward of Palatini-Cartan gravityThe goal of this note is to show that the standard BV formulation of gravity in the Palatini-Cartan formalism is equivalent, using a BV pushforward, to an AKSZ-like version compatible with BFV data…Giovanni Canepa, Alberto S. Cattaneo·Jul 8, 2025SaveLearn