2548 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 establishes the strong resolvent convergence of the anisotropic quantum Rabi model to an effective limiting Hamiltonian in the strong-coupling regime, providing a unified operator-theoretic framework that connects the rotating-wave approximation to the full model and highlights the dominant role of counter-rotating interactions.
This paper constructs and exactly solves a curvature-adapted radial Dunkl Hamiltonian for the group on 3D hyperbolic space under the condition , deriving the discrete spectrum, Jacobi-polynomial eigenfunctions, and normalizability constraints to isolate the specific effects of negative curvature and reflection deformation on bound-state properties.
This paper introduces a kinetic interface model implemented in FESTIM that replaces the flawed assumption of chemical potential continuity with reversible mass-action reaction channels, revealing that hydrogen isotope transport across metal/molten-salt interfaces is governed by dynamic branching ratios and redox states rather than fixed thermodynamic equilibrium, thereby correcting underestimations of permeation flux and ill-posed conditions for multiple isotopes.
This paper resolves a conjecture by proving that for any specified frequency and phase resonance exponents, there exist corresponding parameters for which the Almost Mathieu operator exhibits Anderson localization whenever the coupling strength exceeds the maximum of these exponents.
This paper proposes a parameter-free integral equation for the rate function governing the emptiness formation probability in the ground state of the repulsive Lieb-Liniger Bose gas, deriving it from a dual-field Fredholm-determinant representation and validating it against known limits and extensive numerical hydrodynamic simulations.
This Perspective introduces the off-diagonal low-rank (ODLR) property as a key characteristic of many important matrices in computational chemistry, reviews its mathematical foundations and current applications, and proves its validity for Fock and LMO coefficient matrices to enable new linear-scaling methods for dense, gapless systems.
This paper establishes a comprehensive stochastic variational framework for multiscale surface gravity waves by decomposing the velocity potential into deterministic and stochastic components, deriving coupled path-wise and expected evolution equations that preserve the system's Hamiltonian structure and provide a rigorous foundation for reduced stochastic models and kinetic theory.
This paper develops a kinetic theory for deep-water surface gravity waves interacting with unresolved stochastic velocity fields, demonstrating that stochastic transport can drive spectral evolution through diffusive scattering and effective quartic interactions that often exceed classical resonant four-wave interaction rates in realistic oceanic conditions.
This paper employs the multiscale loop vertex expansion to prove the analyticity and Borel summability of cumulants up to a finite order for the model, a simplest non-trivial super-renormalizable quantum field theory.
This paper establishes a systematic framework for -Morita equivalence of topological orders using -Morita categories, unifying various notions of equivalence and proving that for , the algebraic description of higher Morita theory is equivalent to its realization via module categories, thereby clarifying the relationships among defects in topological orders through the natural emergence of bi-bimodules.