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 contribution presents a total Lagrangian finite element framework for multibody dynamics under large deformations that integrates a compact kinematic representation, a formulation based on the deformation gradient, and a systematic constraint methodology to model the equations of motion for assemblies of deformable bodies under various loads and material models.
This paper demonstrates that in a PT-symmetric open dimer, causality acquires a topological charge at the exceptional point, causing a pole to migrate into the upper half-plane and inducing a sharp, measurable violation of standard Kramers-Kronig relations that scales inversely with the distance from the critical gain-loss threshold.
This paper demonstrates that perturbed contact models on locally compact metric spaces, even when the critical balance between birth and death rates is violated, typically avoid extinction and admit a family of invariant measures describable via the Feynman-Kac formula.
This paper proves that any negative periodic perturbation in mortality within non-local population dynamics models shifts the operator spectrum to the left half-plane, inevitably leading to population extinction in any dimension, even when the birth kernel is non-symmetric and spatially heterogeneous.
This paper develops a trace-Dobrushin theory for quantum channel products to establish conditions for asymptotic replacement and memory loss in both deterministic and stationary random settings, subsequently applying these results to derive infinite-volume limits, boundary stability, and correlation bounds for inhomogeneous matrix product states.
This paper establishes a Generalized Fourier Transform on Riemannian manifolds by resolving spectral degeneracies through symmetry-adapted maximal Abelian commuting sets, thereby constructing a rigorous framework for momentum-space analysis that unifies geometric constraints with unitary mode decompositions.
This paper proves that for the Anderson model on the Bethe lattice in the strong-disorder regime with compactly supported, locally analytic single-site distributions, the root-averaged density of states is absolutely continuous and admits a finite-order, real-analytic expansion where all odd coefficients vanish and higher-order terms are determined by short closed walks on the tree.
This paper establishes a large deviations principle for the supremum of solutions to the Korteweg-de Vries equation with random initial data over polynomial timescales, demonstrating that unusually large wave amplitudes arise primarily from the quasi-synchronization of phases rather than resonant energy exchange, due to the stability of the equation's integrable dynamics.
This paper introduces Unbalanced Schrödinger Bridge (USB), a simulation-free framework that overcomes the limitations of existing continuous Optimal Transport methods by rigorously modeling discrete, jump-like birth-death dynamics at single-cell resolution to reconstruct cellular lineage trajectories from destructive snapshots.
This paper investigates reflection symmetry and Atiyah-Patodi-Singer boundary conditions for twisted Dirac operators on a warped cylinder, establishing that reflection compatibility requires a specific holonomy quantization and demonstrating how spectral flow decomposes into equivariant or mod-two invariants depending on whether the holonomy is fixed or varying.