2560 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 derives a hydrodynamic description for a bulk-driven nonlinear energy diffusion model and demonstrates through simulations that specific driving fields can induce the formation of robust, traveling energy condensates exhibiting continuous time-crystalline order.
This paper investigates the dimer model on two families of non-bipartite torus graphs by establishing the relationship between their Newton polygons and those of underlying bipartite graphs, identifying edge vectors with zig-zag path homology classes, proving the real-rootedness of specific marginal polynomials, and introducing new local moves that preserve dimer partition functions.
This paper establishes the existence of a rare, adiabatically conserved extra invariant in the magnetohydrodynamics of rotating and stratified fluid layers, which is notably linked to the dynamo phenomenon in planets and stars.
This paper presents a general strategy to derive rigorous error bounds and explicit error constants for truncated Baker--Campbell--Hausdorff and Zassenhaus formulas specifically applied to skew-adjoint operators in quantum evolution problems.
This paper develops a unified geometric framework based on the symmetric irreducible representation of SU(4) to model multi-channel collective dissipation in four-level atomic ensembles, deriving compact rate equations that reveal a superlinear power-law scaling of the emitted intensity peak across seven distinct dipole-allowed topologies.
This paper presents a group theoretical analysis demonstrating how the affine symmetry, as a subgroup of affine , governs the projection of root and weight lattice Voronoi cells onto the Coxeter plane to generate specific five-fold symmetric tilings relevant to quasicrystal models.
This paper establishes the Lyapunov stability of finite sums of Lamb dipoles with nonnegative vorticities on the half-plane, provided the dipoles are sufficiently separated and ordered by speed, using a combination of sharp energy estimates and a Lagrangian bootstrapping scheme to quantify circulation and energy exchanges.
This paper presents a systematic numerical analysis of the Eckhaus instability in the one-dimensional Ginzburg-Landau equation, revealing that the evolution from an unstable periodic state to a stable final state proceeds through four distinct regimes: rapid decay of stable perturbations, a latent phase of spectral concentration, a sharp Lyapunov decrease during phase slips, and slow relaxation to stability.
This paper introduces Krylov-Lie algebras as a depth-aware geometric framework for variational quantum algorithms that overcomes the limitations of existing Haar-random theories by providing finite-depth variance formulas, identifying conditions for convergence, and suggesting that non-Haar effects may mitigate barren plateaus to enhance trainability.
This paper resolves the hyperbolic off-center orbit problem for a singular potential by demonstrating that zero-energy trajectories are Euclidean circles orthogonal to the singularity, governed by an symmetry and an inversion duality that extends to quantum mechanics and magnetic classifications on the hyperbolic plane.