3366 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 presents a priori error analysis for a fully discrete, explicit, loosely coupled scheme for the time-dependent Stokes-Biot problem, proving unconditional first-order temporal accuracy and optimal spatial convergence through a discrete energy framework and numerical validation.
This paper establishes the existence and completeness of wave operators, the absence of singular continuous spectrum, and specific eigenvalue accumulation properties for scattering systems governed by non-elliptic unperturbed operators and anisotropic potentials, with applications to invariance principles and time-dependent scenarios.
This paper analyzes the causal structure and geodesic dynamics of horizonless JMN-1 and JNW spacetimes to demonstrate how their distinct singularity types and effective repulsive behaviors produce unique strong-field lensing and shadow signatures that could be observationally distinguished from black holes by instruments like the Event Horizon Telescope.
Motivated by recent works of Lewin, Lieb, and Seiringer, this paper proposes rigorous definitions of the quantum and classical non-uniform electron gas via grand-canonical functionals, establishes them as thermodynamic limits, and analyzes their properties in the presence of an arbitrary lattice-periodic background density.
This paper constructs the $so(N+1,2)$ dynamical symmetry of the quantum Calogero-Coulomb model using Dunkl operators, classifying its wave functions into infinite-dimensional lowest-weight $so(1,2)$ multiplets and expressing the Hamiltonian's linear spectrum via the conformal subalgebra.
This paper establishes the theoretical foundations for the linear and direct sampling methods to qualitatively recover supported cavities in thin elastic plates governed by the biharmonic wave equation, demonstrating through numerical experiments that both methods robustly identify obstacle locations, with the direct sampling method offering superior stability and computational efficiency.
This paper introduces a linear-algebraic framework that utilizes logarithmic variables to systematically determine independent dimensionless quantities and eliminate redundancies in dimensional analysis, particularly for complex systems with numerous variables or implicit constraints where traditional elimination methods are impractical.
This paper derives exact bound-state solutions and energy spectra for a spin-1/2 fermion governed by the Dirac equation with a general combination of scalar, vector, and tensor Coulomb potentials in 3+1 dimensions, establishing a direct mapping between planar and spherical problems while validating existing results and introducing new cases involving broken spin and pseudospin symmetries.
This paper presents a novel classification of unitarizable supermodules over the special linear Lie superalgebra by utilizing an algebraic quadratic Dirac operator and a corresponding Dirac inequality.
This paper demonstrates that non-Hermiticity in a two-qubit asymmetric Heisenberg system can induce a thermal entanglement phase transition, where maximal entanglement emerges above a critical non-Hermiticity threshold due to ground state degeneracy rather than exceptional points, while proposing a singular-value-decomposition approach for computing entanglement in such bi-orthogonal systems.