2619 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 solves the Riemann-Hilbert problem for higher-rank Mathieu opers on the twice-punctured sphere by expressing solutions via a non-linear integral equation, thereby proving the Nekrasov-Rosly-Shatashvili conjecture linking oper generating functions to the quantum Toda chain's Yang-Yang function and interpreting these results within the framework of the Analytic Langlands Correspondence.
This paper investigates a first boundary value problem for a second-order partial differential equation involving the Prabhakar fractional derivative by constructing an explicit Green's function through a Volterra-type integral equation reduction, thereby deriving a closed-form solution representation and proving its existence and uniqueness.
This paper introduces a quantum Viterbi decoding algorithm for hidden quantum Markov models that optimizes over continuous manifolds of pure quantum effects to achieve a strict quantum advantage in decoding scores over classical strategies, offering a new primitive for quantum sequential decision-making and machine learning.
This didactic article derives Gutzwiller's trace formula from the Feynman path integral to explain how classical periodic orbits determine quantum energy spectra in chaotic systems and their connection to random matrix theory.
This paper establishes the existence of time-periodic weak solutions for a fluid-structure interaction system coupling incompressible Navier-Stokes equations with a nonlinear Koiter plate model by introducing a novel single Leray-Schauder fixed-point strategy that overcomes the convexity limitations of previous two-stage approaches.
This paper systematically establishes the equivalence between two variational formulations of magnetostatics—one using magnetization and magnetic field, and the other using only magnetic induction—demonstrating that this link remains stable in coupled magnetoelastic models despite the absence of standard convex duality and the lack of preserved convexity or coercivity in the transformation.
This paper proves the weak cosmic censorship conjecture for circularly symmetric Einstein-scalar field systems in dimensions with a negative cosmological constant by demonstrating that generic initial data evolve into spacetimes free of naked singularities, a result underpinned by the existence of a mass gap and the instability of naked singularities due to infinite blueshift.
This paper proves the Gang-Kim-Yoon integrality conjecture for all torus knots and non-negative integers by introducing Verlinde numbers derived from the modular S-matrix, establishing their recursion formulas, and demonstrating how adjoint Reidemeister torsions can be recovered from the Hessian of a birational model of the character variety.
This paper introduces Interval Quantum Mechanics (IQM), a finite-precision framework that replaces idealized point states with "quantum parcels" (open sets of density matrices) to resolve foundational paradoxes like the von Neumann entropy dilemma and wave-particle duality by treating quantum states as epistemic geometric objects that evolve deterministically and refine through measurement, while recovering standard quantum predictions in the infinite-precision limit.
This paper presents a complete analysis of the glass transition in the self-overlap-corrected quantum Sherrington-Kirkpatrick model under a transverse magnetic field, determining the phase boundary between glassy and paramagnetic phases through a simplified Parisi variational principle that relies solely on classical order parameters.