From Yang-Mills to Yang-Baxter: In Memory of Rodney Baxter and Chen--Ning YangThe year 2025 marked the passing of two towering figures of twentieth-century mathematical physics, Rodney Baxter and Chen-Ning Yang. Yang reshaped modern physics through the introduction of…Bai-Ling Wang·Dec 30, 2025SaveLearn
Quasicrystalline Gibbs states in 4-dimensional lattice-gas models with finite-range interactionsWe construct a four-dimensional lattice-gas model with finite-range interactions that has non-periodic, "quasicrystalline" Gibbs states at low temperatures. Such Gibbs states are probability…Jacek Miȩkisz, Siamak Taati·Dec 30, 2025SaveLearn
Quantum two-dimensional superintegrable systems in flat space: exact-solvability, hidden algebra, polynomial algebra of integralsIn this short review paper the detailed analysis of six two-dimensional quantum superintegrable systems in flat space is presented. It includes the Smorodinsky-Winternitz potentials I-II (the…Alexander V Turbiner, Juan Carlos Lopez Vieyra, Pavel Winternitz·Dec 30, 2025SaveLearn
On spectral equations for an evolution operator of a q-oscillator latticeWe propose a set of algebraic equations describing eigenvalues and eigenstates of a relativistic evolution operator for a two-dimensional q-oscillator Kagom\'e lattice. Evolution operator is…Sergey Sergeev·Dec 30, 2025SaveLearn
Port--Hamiltonian Diffusion Models: A Control-Theoretic Perspective on Generative ModelingDiffusion models have recently achieved remarkable success in generative modeling, yet they are commonly formulated as black-box stochastic systems with limited interpretability and few structural…Majid Darehmiraki·Dec 29, 2025SaveLearn
The five-vertex model as a discrete log-gasWe consider the five-vertex model on a rectangular domain of the square lattice, with the so-called `scalar-product' boundary conditions. We address the evaluation of the free-energy density of the…Filippo Colomo, Michelangelo Mannatzu, Andrei G. Pronko·Dec 29, 2025SaveLearn
On construction of differential Z-graded varietiesGiven a commutative unital algebra O, a proper ideal I in O, and a positively graded differential variety over O/ I, we provide a $…Aliaksandr Hancharuk, Ruben Louis·Dec 29, 2025SaveLearn
Lectures on Gauge theories and Many-Body systemsThese lectures study two correspondences between gauge theories and integrable many-body systems. The first arises from infinite-dimensional Hamiltonian reduction and relates gauge-theoretic dynamics…Igor Chaban, Nikita Nekrasov·Dec 28, 2025SaveLearn
Non-SUSY physics and the Atiyah-Singer index theoremThe Atiyah-Singer index theorem, a cornerstone of modern mathematics, has traditionally been derived from supersymmetric (SUSY) physics. This paper demonstrates a direct derivation from…Shunrui Li, Yang Liu·Dec 28, 2025SaveLearn
Field Theory via Higher Geometry II: Thickened Smooth Sets as Synthetic FoundationsThis is the second in a series of papers that aim to develop rigorous and most encompassing foundations for field theory, where in the first installment, we laid out the natural formulation of…Grigorios Giotopoulos, Hisham Sati·Dec 28, 2025SaveLearn
The stochastic six vertex model and discrete orthogonal polynomial ensemblesStochastic growth models in the Kardar-Parisi-Zhang (KPZ) universality class exhibit remarkable fluctuation phenomena. While a variety of powerful methods have led to a detailed understanding of…Promit Ghosal, Guilherme L. F. Silva·Dec 27, 2025SaveLearn
The Loring--Schulz-Baldes Spectral Localizer RevisitedThe spectral localizer, introduced by Loring in 2015 and Loring and Schulz-Baldes in 2017, is a method to compute the (infinite volume) topological invariant of a quantum Hamiltonian on d, as…Gregory Berkolaiko, Jacob Shapiro, Beyer Chase White·Dec 26, 2025SaveLearn
Chaos, Ito-Stratonovich dilemma, and topological supersymmetryIt was recently established that the formalism of the generalized transfer operator (GTO) of dynamical systems (DS) theory, applied to stochastic differential equations (SDEs) of arbitrary form,…Igor V. Ovchinnikov·Dec 25, 2025SaveLearn
Quantum Mean-Fields Spin Systems in a Random External FieldIn this work, we consider general exchangeable quantum mean-field Hamiltonian such as the prominent quantum Curie-Weiss model under the influence of a random external field. Despite being arguably…Chokri Manai·Dec 25, 2025SaveLearn
On Rayleigh scattering in the massless Nelson modelAsymptotic completeness of Rayleigh scattering in models of atoms and molecules of non-relativistic QED is expected, but for a proof we still lack sufficient control on the number of emitted soft…Marcel Griesemer, Valentin Kussmaul·Dec 24, 2025SaveLearn
Hamilton-Jacobi as model reduction, extension to Newtonian particle mechanics, and a wave mechanical curiosityThe Hamilton-Jacobi equation of classical mechanics is approached as a model reduction of conservative particle mechanics where the velocity degrees-of-freedom are eliminated. This viewpoint allows…Amit Acharya·Dec 24, 2025SaveLearn
Limits of Equi-Affine Equi-Distant Loci of Planar Convex Domains with Two Non-Parallel AsymptotesIn this note, we introduce equi-affine invariants by averaging over the space of tropical structures of fixed covolume. Applied to the tropical distance series, this construction produces a family of…Nikita Kalinin, Mikhail Shkolnikov·Dec 24, 2025SaveLearn
Renormalized tropical field theoryWe introduce tropical scalar field theory as a model for renormalizable quantum field theory, and examine in detail the case of quartic self-interaction and internal O(N) symmetry. This model…Paul-Hermann Balduf, Erik Panzer·Dec 24, 2025SaveLearn
Propagation Estimates for the Boson Star EquationWe consider the boson star equation with a general two-body interaction potential w and initial data 0 in a Sobolev space. Under general assumptions on w, namely that w decomposes as a…Sébastien Breteaux, Jérémy Faupin, Viviana Grasselli·Dec 23, 2025SaveLearn
Exponential Decay outside of the Light Cone for the Pseudo-Relativistic Non-Autonomous Schr\"odinger EquationWe establish a maximal velocity bound for a pseudo-relativistic quantum particle in an external time-dependent potential. Our estimate shows that the probability for the particle, starting in a…Sébastien Breteaux, Jérémy Faupin, Viviana Grasselli·Dec 23, 2025SaveLearn
On the Hartree-Fock phase diagram for the two-dimensional Hubbard modelWe propose an analytical method for the construction of Hartree-Fock phase diagrams for the (fermion) Hubbard model and various generalizations thereof. Such phase diagrams are traditionally…Christophe Charlier, Edwin Langmann, Jonatan Lenells·Dec 23, 2025SaveLearn
Second-species dynamics in the restricted planar circular three body problem: chaos, final motions and periodic orbitsConsider the Restricted Planar Circular Three Body Problem (RPC3BP), which models the motion of a massless particle (Asteroid) under the gravitational influence of two massive bodies (the primaries)…Marcel Guardia, José Lamas, Tere M-Seara·Dec 23, 2025SaveLearn
Critical Hermitian matrix model with external source and Boussinesq hierarchyWe consider the random Hermitian matrix model of dimension 2n, with external source, defined by the probability density function equation* 1Z2n (M) α…Dong Wang, Shuai-Xia Xu·Dec 23, 2025SaveLearn
Localization of the eigenfunctions of a Bloch-Torrey operator on the half-planeWe consider a non-self adjoint operator of the form -h2 + i(V(x) + α(x)y) on the upper half plane y > 0 with Dirichlet boundary conditions on \y = 0\ with V ≥ 0, V…Martin Averseng, Nicolas Frantz, Frédéric Hérau et al.·Dec 23, 2025SaveLearn
Group-Theoretical Origin of the Sectoral-Tesseral-Zonal Trichotomy in Spherical HarmonicsThe spherical harmonics Ym fall into three families -- sectoral ( = |m|), tesseral ( > |m| > 0), and zonal (m = 0) -- which exhibit fundamentally different behaviour under…Mustafa Bakr, Smain Amari·Dec 23, 2025SaveLearn