3340 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 characterizes the transition asymptotics of real solutions to the sinh-Gordon Painlevé III equation as both the independent variable and the monodromy parameter tend to infinity, detailing how the solutions evolve from singular behavior to elliptic and finally to trigonometric asymptotics depending on the scaling regime.
This paper establishes the exact exponential cost rate for nonlinear remote stabilization of an Aubry--André chain as the off-spectral Lyapunov exponent at a reflected band edge, proving this identity unconditionally for all phases in the metallic and critical regimes and for almost every phase in the localized regime under specific conditions.
This paper identifies a new sixteen-fold family of (2+1)D fermionic topological orders characterized by a mod 16 't Hooft anomaly of a one-form symmetry, which allows for intrinsically fermionic anyon spins and can be realized as gapped boundaries of twisted (3+1)D fermionic SPT phases via lattice models.
This paper proves that the two-dimensional Blume-Emery-Griffiths model at the Ferromagnetic-Antiquadrupolar-Disordered (FAD) triple point on the square lattice possesses a unique Gibbs measure at any temperature, thereby establishing the absence of phase transitions through a random-cluster representation coupled with Bernoulli site percolation.
This paper solves large- Yang--Mills theory on at strong coupling for the heat-kernel action by proving the existence of a master field with exponentially local coefficients and an area-law upper bound, utilizing a novel rooted heat-kernel master loop equation that closes on an extended space of decorated loop observables.
This paper establishes the analytic foundation for noncommutative anisotropic diffusion in Hilbert spaces by deriving a consistent energy form that accounts for non-commuting anisotropy and covariance operators, and proving key results including form closability, well-posedness of forward dynamics, Mosco stability, and a general weak-bridge theorem linking backward drifts to entropy dissipation.
This paper proposes a cohomological framework for computing conformal anomalies, demonstrating that the leading perturbative beta function in current-current deformed two-dimensional conformal field theories corresponds to the cocycle coefficient obstructing the deformation of the Virasoro module structure, thereby offering a novel perspective and efficient tool for calculating higher-order beta function coefficients.
This paper establishes a unified geometric framework linking split attractor flows, Hessian flows, and spectral networks to rigorously prove their orthogonality and duality, thereby enabling the systematic reconstruction of BPS spectra across diverse theories and yielding new closed-form results for Argyres-Douglas models and tropical disk counts.
This paper derives exact analytical solutions for a heterogeneous Cattaneo-Vernotte diffusion equation with an exponential diffusion coefficient in terms of modified Bessel functions and proves that these solutions constitute valid probability density functions.
This paper presents a GPU-accelerated PDE-constrained optimization framework that jointly recovers full-field displacement and force distributions from sparse sensor measurements with significantly higher accuracy than modal expansion methods, as demonstrated on increasingly complex structural examples ranging from a cantilever plate to a nuclear reactor pressure vessel.