3210 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 develops an effective radial framework for charged spinless particles in collinear electric and magnetic fields under a weak-field approximation, utilizing Tridiagonal representation approaches in Laguerre and Jacobi bases to derive new analytical energy spectra and numerical benchmarks for field-modified potentials.
This paper identifies a directional tangency mechanism driven by the geometric alignment of source singularities with the Fermi surface that causes anomalous, algebraic far-field decay in two-dimensional Schrödinger equations, contrasting with the super-algebraic decay observed when such alignment is absent.
This paper establishes minimal geometric matching rules, utilizing either colored arrows or colored squares, to enforce the three-dimensional "Chair" monotile to form a strongly aperiodic tiling by uniquely composing into larger "Superchairs," thereby facilitating the search for physical realizations of such structures.
This paper establishes a Lee-Yang zero-freeness theorem for a broad class of interacting fermion models, including the attractive and repulsive Hubbard models, which guarantees the absence of phase transitions under nonzero local external fields and enables provably efficient quantum algorithms for estimating their ground-state energies.
This paper establishes a linear variance bound for the height of the standard continuous-time ballistic deposition process in all dimensions by adapting Aldous's martingale argument to derive tail bounds on first hitting times and applying Penrose's duality theorem.
This paper proposes an implementation-friendly, pressure-robust, and superconvergent staggered discontinuous Galerkin scheme for Stokes and Navier-Stokes equations on Cartesian grids, utilizing piecewise-constant spaces with static condensation and a novel discrete convection term to achieve second-order accuracy and unconditional energy stability.
This paper determines the maximum stable volume of bubbles attached to flat surfaces and circular cavities by solving the Young-Laplace equation to identify three distinct detachment modes, with predictions that align well with experimental data across various bubble types and extend to pendant drops.
This paper derives exact scaling laws for the ageing behavior of the voter model on a fractal substrate, demonstrating that while the dynamic and autocorrelation exponents depend on both the geometric and spectral dimensions, the explicit dynamic scaling functions are determined solely by the spectral dimension.
This paper establishes the existence and uniqueness of fundamental solutions for the Klein-Gordon equation with Robin boundary conditions on globally hyperbolic spacetimes with timelike boundaries, characterizes their wavefront sets, and constructs Robin-Hadamard two-point correlation functions by extending the Hadamard parametrix to include reflected null rays, thereby proving a counterpart to Radzikowski's theorem in this setting.
Motivated by OpenAI's reported finite-time singularity, this paper demonstrates that driving a pseudospin Hopf texture in a Bose-Einstein condensate with a Navier-Stokes blow-up analog induces a fold cascade of preimage pair creation and annihilation, where the initial one-to-three transition follows the square-root opening characteristic of a Thom catastrophe while conserving the total Hopf charge.