3210 papers
Mathematical physics sits at the fascinating intersection where abstract equations meet the fundamental laws of our universe. This field uses rigorous mathematical tools to model everything from the behavior of subatomic particles to the curvature of spacetime, turning complex theories into testable predictions. It is the language through which physicists describe reality, bridging the gap between pure mathematics and physical observation.
On Gist.Science, we process every new preprint published in this category on arXiv to make these dense studies accessible to everyone. Whether you are a specialist or a curious reader, you will find both plain-language overviews and detailed technical summaries for each paper. Below are the latest mathematical physics papers from arXiv, curated to help you explore the cutting edge of theoretical science.
This paper identifies partial autocorrelation coefficients as natural, independent coordinates on the convex region of admissible two-point correlation functions, thereby simplifying the calculation of constraints and providing a classical statistical interpretation for the Fisher -transformation used in likelihood analyses.
This paper constructs smooth, non-trivial one-parameter families of magnetohydrostatic equilibria on solid tori for every sufficiently large that possess only rotational symmetry, thereby providing counterexamples to Grad's conjecture regarding the necessity of plane-reflection, axial, or helical symmetries, with results further validated by a Lean 4 formalization.
This paper demonstrates that for two-dimensional lattice Hamiltonians and magnetic Schrödinger operators within a mobility gap, a nonzero bulk topological index guarantees that the entire energy interval constitutes the absolutely continuous spectrum of the corresponding half-space operator, with a spectral multiplicity bounded below by the magnitude of the index.
This paper consolidates the renormalized Lambert-W branch-point cascade and finite-time amplification mechanisms to support the claim that the 3D Navier-Stokes equations on lose smoothness in finite time from smooth initial data.
This paper establishes a deep topological correspondence between GKP codes, their Clifford gates, and algebraic curves by demonstrating how symplectic automorphisms of GKP lattices relate to the mapping class group of genus- surfaces, thereby providing a topological interpretation of fault tolerance where logical operations arise as monodromies in the space of lattice realizations.
This paper establishes a uniform bound on the influence matrix for ferromagnetic Ising models at the tree uniqueness threshold, thereby removing a logarithmic factor from previous results and proving that zero-field single-site Glauber dynamics mixes in polynomial time within a specific supercritical window.
This paper presents a Bethe-ansatz-type construction for eigensections and eigenvalues of -curvature operators associated with KZ-type additive discrete flat connections in characteristic , expressing these eigensections as finite discrete hypergeometric sums over the lattice .
This paper develops a functorial framework for defects in Abelian Chern-Simons theory by utilizing categorical TQFTs and the Alterfold construction to clarify bulk realizations, establish a dictionary for topological boundaries and domain walls, identify finite quadratic modules as the governing invariants, and demonstrate that proposed Abelian Chern-Simons dualities do not constitute genuine TQFT dualities.
This paper introduces a novel "Schrödinger-Dirichlet" equation for interacting bosons, utilizing harmonic analysis on the multiplicative group of positive rationals to model a nonlinear, nonlocal evolution that generates entanglement from separable states, distinguishing it from conventional mean-field approaches.
This paper employs -convergence to demonstrate that rigid polycrystalline structures in charge-dependent hard-sphere ionic systems emerge as low-energy configurations, yielding a continuum theory where anisotropic interfacial energy concentrates at grain boundaries determined by misorientation, translation misfit, and interface normal.