1605 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 a classical Heun observable as the most general bilinear combination of two observables satisfying classical Askey-Wilson relations, demonstrating that its associated Hamiltonian dynamics are governed by quartic differential equations and elliptic functions, thereby providing an algebraic mechanism that links classical Leonard pairs to elliptic solvability.
This paper generalizes the theory of finitely correlated states to disordered systems driven by ergodic topological dynamics, demonstrating that a specific disordered AKLT state exhibits a closed bulk spectral gap, almost surely exponentially decaying correlations, and a time-reversal invariant Tasaki index of $-1$.
This paper provides an equivalent characterization of the previously unknown constant in the leading order term of the lattice Yang-Mills free energy by adjusting boundary conditions, thereby enabling its explicit computation.
This paper proves that the strongly coupled large-N Principal Chiral Model in the double-scaling regime exhibits maximal transcendentality to all orders, with its vacuum-energy expansion coefficients forming polynomials in odd zeta values that reveal deeper number-theoretic regularities.
This paper employs the covariant coframe/spin-connection formalism in teleparallel gravity to reconstruct static, spherically symmetric spacetime solutions sourced by Chaplygin and polytropic fluids, revealing diverse geometric branches ranging from stellar interiors and black holes to traversable wormholes while analyzing their horizon structures, energy conditions, and stability within a unified framework.
This paper utilizes the exactly solvable 't Hooft model to rigorously demonstrate that a PT-symmetric deformation drives meson states to an exceptional point at a precisely calculable confinement-scaled threshold, causing a definitive breakdown of analyticity in the causal response function characterized by a square-root singularity and linear time-domain growth.
This paper establishes a unified contact Tulczyjew formalism on skew algebroids that intrinsically explains dissipative dynamics through a modified morphism and extends this framework to both continuous Euler-Lagrange-Herglotz equations and discrete contact variational integrators.
This paper resolves a problem posed by A. Agrachev regarding the minimum number of traversals required for a circle in to admit a deformation with a nondegenerate Frenet frame, revealing that the answer depends on the chosen topology and introducing decorated turn data to characterize accessibility via constant or time-dependent controls across various dimensions.
This paper introduces a weighted least action principle for the geometric optics limit of Maxwell equations that determines the complete bundle of Fresnel rays connecting two planes based on intensity measurements, thereby enabling the reconstruction of electromagnetic wave phases through reciprocity.
This paper reviews random matrix theory approaches to chaotic wave scattering and transport in open systems, emphasizing universal statistics and non-perturbative methods derived from effective non-Hermitian Hamiltonians to describe scattering matrices, time delays, and resonance phenomena.