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 classifies the sparse set of Fano and reflexive polytopes arising from quasi-finite Feynman integrals, demonstrating their intrinsic connection to Calabi-Yau varieties through the geometric structures encoded by Symanzik polynomials.
This paper investigates the connection problem for a class of -th order linear differential equations related to the quantum Toda chain, deriving quantization conditions based on monodromy data that validate predictions from topological string/spectral theory duality for deformed Schrödinger operators.
This paper proposes a topology-aware postprocessing framework that utilizes persistent homology to automatically determine optimal thresholds for qualitative acoustic inverse scattering indicators, thereby enabling robust reconstruction of scatterers with complex topologies like multiple components or holes.
This paper establishes a rigorous functional-analytic framework for the data-driven stress problem under purely homogeneous normal Neumann boundary conditions, proving the existence and uniqueness of solution equivalence classes by leveraging the topological properties of the divergence operator and the proximinality induced by finite experimental data sets.
This paper proposes a testable, Halilsoy-inspired extension to the standard Newtonian lunar tidal model that introduces an alpha-dependent off-diagonal residual component, which rotates the tidal eigenframe and generates a distinct 45-degree cross-tidal signature absent in the classical diagonal tensor description.
This paper demonstrates that standalone relativistic hydrodynamic effective field theories are inherently acausal and necessitates the inclusion of transient ultraviolet modes to restore causality while preserving the correct late-time hydrodynamic behavior.
This paper presents a unified, probabilistic "black box" proof based on random walk techniques that establishes mean-field near-critical behavior and specific decay rates for the two-point functions of various high-dimensional lattice statistical mechanical models, including self-avoiding walks, percolation, and spin systems.
This paper defines new families of Kuramoto models associated with bounded symmetric domains of types I, II, and III by extending the Watanabe-Strogats construction to these domains and their Bergman-Shilov boundaries, thereby generalizing existing models like the Lohe unitary and spherical models.
This paper analyzes a one-dimensional three-body quantum system with zero-range interactions, demonstrating that for an attractive potential and small mass ratios, the eigenvalues below the essential spectrum follow a specific asymptotic expansion involving Airy function extrema or zeros depending on particle statistics, while also characterizing the system's essential spectrum.
This paper establishes a theoretical framework for identifying non-smooth spectral bifurcations in the interior transmission eigenvalue problem, specializes the analysis to radially symmetric geometries, and validates these findings through a novel adaptive contour eigensolver that accurately tracks eigenvalue trajectories under parameter variation.