On the Lieb--Wehrl Entropy conjecture for SU(N,1)We investigate the sharp functional inequalities for the coherent state transforms of SU(N,1). These inequalities are rooted in Wehrl's definition of semiclassical entropy and his conjecture about…Mandeep Singh·Jan 17, 2025SaveLearn
Relating the modular Hamiltonian to two-point functionsWe consider the modular Hamiltonian associated to standard subspaces for a free scalar field in a globally hyperbolic spacetime in an arbitrary Gaussian state. We show how the modular Hamiltonian is…Markus B. Fröb·Jan 16, 2025SaveLearn
Calculus with combinatorial differential forms for fluid flow analysis in porous and fractured mediaThe fabric of porous and fractured media contains solid regions (grains) and voids. The space conducting fluids is a system of connected voids with variable geometries. Relative to the grain sizes,…Changhao Liu, Kiprian Berbatov, Majid Sedighi et al.·Jan 15, 2025SaveLearn
Integrable deformations of principal chiral model from solutions of associative Yang-Baxter equationWe describe deformations of the classical principle chiral model and 1+1 Gaudin model related to GLN Lie group. The deformations are generated by R-matrices satisfying the associative…D. Domanevsky, A. Levin, M. Olshanetsky et al.·Jan 15, 2025SaveLearn
Operational solutions for the generalized Fokker-Planck and generalized diffusion-wave equationsThe evolution operator method is used to solve the generalized Fokker-Planck equations and the generalized diffusion-wave equations in the (1+1) dimensional space in which x∈R and…K. Górska·Jan 14, 2025SaveLearn
Renormalising Feynman diagrams with multi-indicesIn this work, we provide a method to obtain the renormalised measure in quantum field theory directly from the renormalisation of the expansion of the original measure. Our approach is based on BPHZ…Yvain Bruned, Yingtong Hou·Jan 14, 2025SaveLearn
Solution to SU(n+1) Toda system generated by spherical metricsUsing the correspondence between solutions to the SU(n+1) Toda system on a Riemann surface and totally unramified unitary curves, we show that a spherical metric ω generates a family of…Yiqian Shi, Chunhui Wei, Bin Xu·Jan 14, 2025SaveLearn
Wasserstein distances and divergences of order p by quantum channelsWe introduce a non-quadratic generalization of the quantum mechanical optimal transport problem introduced in [De Palma and Trevisan, Ann. Henri Poincar\'e, 22 (2021), 3199-3234] where quantum…Gergely Bunth, József Pitrik, Tamás Titkos et al.·Jan 14, 2025SaveLearn
Categorical quantum symmetries and ribbon tensor 2-categoriesIn a companion work on the combinatorial quantization of 4d 2-Chern-Simons theory, the author has constructed the Hopf category of quantum 2-gauge transformations C=UqG…Hank Chen·Jan 14, 2025SaveLearn
The Wigner Little Group for Photons Is a Projective SubalgebraThis paper presents the Geometric Algebra approach to the Wigner little group for photons using the Spacetime Algebra, incorporating a mirror-based view for physical interpretation. The shift from a…Moab Croft, Hamish Todd, Edward Corbett·Jan 14, 2025SaveLearn
The one-dimensional equilibrium shape of a crystalOptimizing the free energy under a mass constraint may generate a convex crystal subject to assumptions on the potential g(0)=0, g 0. The general problem classically attributed to Almgren is…Emanuel Indrei·Jan 14, 2025SaveLearn
Polyakov-Alvarez Formula for Curvilinear Polygonal Domains with SlitsWe consider the ζ-regularized determinant of the Friedrichs extension of the Dirichlet Laplace-Beltrami operator on curvilinear polygonal domains with corners of arbitrary positive angles. In…Ellen Krusell·Jan 13, 2025SaveLearn
The BCFW Tiling of the ABJM AmplituhedronThe orthogonal momentum amplituhedron Ok was introduced simultaneously in 2021 by Huang, Kojima, Wen, and Zhang, and by He, Kuo, and Zhang, in the study of scattering amplitudes of ABJM theory. It…Michael Oren-Perlstein, Ran Tessler·Jan 13, 2025SaveLearn
Instantons with continuous conformal symmetries: Hyperbolic and singular monopoles and more, oh my!Throughout this paper, we comprehensively study instantons with every kind of continuous conformal symmetry. Examples of these objects are hard to come by due to non-linear constraints. However, by…C. J. Lang·Jan 13, 2025SaveLearn
Momentum coupling of classical atomsA new method, dual-space cluster expansion, is proposed to study classical phases transitions in the continuum. It relies on replacing the particle positions as integration variables by the momenta…Andras Suto·Jan 13, 2025SaveLearn
Free energy of spherical Coulomb gases with point chargesWe consider two-dimensional Coulomb gases on the Riemann sphere with determinantal or Pfaffian structures, under external potentials that are invariant under rotations around the axis connecting the…Sung-Soo Byun, Nam-Gyu Kang, Seong-Mi Seo et al.·Jan 13, 2025SaveLearn
Segal-Bargmann transforms and generalized Weyl algebras associated with the Meixner class of orthogonal polynomialsMeixner (1934) proved that there exist exactly five classes of orthogonal Sheffer sequences: Hermite polynomials which are orthogonal with respect to Gaussian distribution, Charlier polynomials…Chadaphorn Kodsueb, Eugene Lytvynov·Jan 13, 2025SaveLearn
Dualities in random matrix theoryDuality identities in random matrix theory for products and powers of characteristic polynomials, and for moments, are reviewed. The structure of a typical duality identity for the average of a…Peter J. Forrester·Jan 13, 2025SaveLearn
Vortices for lake equations (review with questions and speculations)The `lake equation' on a planar domain D with bathymetry b(x,y) is given by $ ∂t u + (u · grad) u= - grad\, p \,, \,\, div (b u) = 0 \,,\, with\,\, u …Jair Koiller·Jan 12, 2025SaveLearn
Lecture notes on conformal field theoryThese are the notes on two-dimensional conformal field theory, based on a lecture course for graduate math students, given by P.M. in fall 2022 at the University of Notre Dame. These notes are…Pavel Mnev·Jan 11, 2025SaveLearn
PT-Symmetric SU(2)-like Random Matrix Ensembles: Invariant Distributions and Spectral FluctuationsWe consider an ensemble of 2× 2 normal matrices with complex entries representing operators in the quantum mechanics of 2 - level parity-time reversal (PT) symmetric systems. The randomness of…Stalin Abraham, A. Bhagwat, Sudhir Ranjan Jain·Jan 11, 2025SaveLearn
Mean-field behavior of the quantum Ising susceptibility and a new lace expansion for the classical Ising modelThe transverse-field Ising model is widely studied as one of the simplest quantum spin systems. It is known that this model exhibits a phase transition at the critical inverse temperature…Yoshinori Kamijima, Akira Sakai·Jan 11, 2025SaveLearn
Combinatorial quantization of 4d 2-Chern-Simons theory I: the Hopf category of higher-graph states2-Chern-Simons theory, or more commonly known as 4d BF-BB theory with gauged shift symmetry, is a natural generalization of Chern-Simons theory to 4-dimensional manifolds. It is part of the bestiary…Hank Chen·Jan 11, 2025SaveLearn
A primer of the complex WKB method, with application to the ODE/IM correspondenceIn these lectures, we provide an introduction to the complex WKB method, using as a guiding example a class of anharmonic oscillators that appears in the ODE/IM correspondence. In the first three…Gabriele Degano, Davide Masoero·Jan 10, 2025SaveLearn
Skein Construction of Balanced Tensor ProductsThe theory of tensor categories has found applications across various fields, including representation theory, quantum field theory (conformal in 2 dimensions, and topological in 3 and 4 dimensions),…Manuel Araújo, Jin-Cheng Guu, Skyler Hudson·Jan 10, 2025SaveLearn