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 introduces and characterizes recurrence and transience for graphs over non-Archimedean ordered fields by relating them to random walks on real directed graphs, ultimately expressing these properties in terms of a capacity-related quantity.
This paper develops a theoretical framework for the error convergence of the stitching approximation in Green's function calculations via the Lanczos algorithm, demonstrating that the convergence rate depends on the decay of subleading Lanczos coefficients and the smoothness of the spectral function, while also deriving a formula linking the spectral function at the origin to continued fraction coefficients to estimate the diffusion constant in the mixed-field Ising model.
This paper investigates the metastable behavior of the disordered Curie-Weiss-Potts model with unbounded random interactions under Glauber dynamics, establishing its metastability and deriving the asymptotic properties of the transition time ratio relative to the non-disordered model by combining potential-theoretic methods with concentration of measure techniques.
This paper proves that massive Dirac particles in one dimension, guided by a Gaussian wave packet, exhibit trajectories with constant asymptotic momentum and energy determined by their initial position, utilizing the stationary phase approximation to demonstrate that negative-energy particles travel in the opposite direction of their momentum.
This paper presents the first construction of exact, positive-energy, normalizable Dirac wave packets in an attractive Coulomb-like potential, revealing unique families that exhibit spin-independent probability densities, a freezing of time evolution at critical coupling, and a direct correspondence to free-Schrödinger Hermite-Gauss wave packets in the nonrelativistic limit.
This paper establishes that macroscopic elastic surface instability in soft materials is fundamentally a topological phase transition, where the onset of wrinkling corresponds to a shift from a trivial to a non-trivial topological phase characterized by a quantized winding number and the emergence of a robust zero-energy edge state.
This paper provides a geometric interpretation of the pole-zero formalism for characterizing the topology of inversion-symmetric one-dimensional periodic media by demonstrating that the associated invariant arises from the monodromy of a Real eigenline bundle constructed on the universal covering of the Brillouin circle.
This paper establishes a nonlinear graviton theorem for higher-spin self-dual gravity by demonstrating that small deformations of the complex structure in non-projective twistor space generate an infinite-dimensional manifold of holomorphic planes, which encodes solutions to the theory and reveals its integrability through a Lax pair.
This paper demonstrates both analytically and numerically that adding a third fluctuating species to a two-population neuronal model can either enhance or suppress noise-induced quasi-cycles, thereby offering an extended framework for studying synchronization beyond the traditional Kuramoto setting.
This paper demonstrates that, unlike in classical fluid dynamics where shock profiles are monotone, relativistic pure-radiation fluids with viscosity can exhibit shock waves with continuous profiles that oscillate in all variables.