2563 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 demonstrates that within an optimization-driven framework for linearly elastic solids, minimizing the work of external loads causes initially volumetric growth to concentrate into singular surface or interface distributions, thereby providing a variational mechanism for the selection of surface growth over volumetric growth.
This paper provides rigorous counterexamples demonstrating that the wave operators for one-dimensional Schrödinger operators with bounded, compactly supported potentials are unbounded on and in generic cases and specific exceptional cases, thereby completing the characterization of their boundedness.
This paper derives an exact and explicit formula for the average entanglement entropy of the Bogoliubov-Kubo-Mori random state ensemble by utilizing properties of its normalization constant, thereby establishing a framework for calculating higher-order cumulants.
This paper proposes an online spectral deflation strategy that accelerates the solution of parameter-dependent, state-constrained optimal control problems by reusing a single full-domain reference eigenbasis to precondition Krylov subspace solvers on varying inactive sets, achieving significant reductions in iteration counts and wall time across diverse PDE benchmarks.
This paper derives explicit formulae for the number of regular even-valent graphs with fixed minimal embedding genus (specifically for ) and varying valence and vertex counts, extending previous results for genus 0 and 1 while also providing asymptotic analysis and a structural conjecture for higher genera.
This paper investigates how nonsymplectic congruence transformations, exemplified by Bopp's shift in noncommutative phase space, preserve the Fisher-Rao distance of Gaussian states while altering their entanglement, and proposes a photocurrent-based gedankenexperiment to detect these effects on state distinguishability.
This paper employs macroscopic fluctuation theory to derive exact typical charge probability distributions for stochastic charged cellular automata, successfully capturing the anomalous fluctuations arising from the coexistence of normal and convective diffusion in these linearly degenerate systems.
This paper investigates a generalized fractional Rabi model using Caputo derivatives to demonstrate how fractional temporal nonlocality induces controllable damping and dephasing in two-level quantum systems, offering new experimental signatures and pathways for exploring memory effects in materials like graphene and topological chains.
This paper introduces a generalization of a non-stationary difference equation linked to the affine Laumon space, conjecturing that its solutions correspond to affine Laumon partition functions and verifying this connection by demonstrating that the equation reduces to the Fuji-Suzuki-Tsuda system in the four-dimensional limit.
This paper establishes a topological classification of non-orientable Weyl semimetals using twisted (co)homology groups and exact sequences, thereby providing a coordinate-independent explanation for charge cancellation and predicting novel phenomena across non-Hermitian and inversion-symmetric systems.