1985 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 generalizes the construction of Lax pairs and integrability to higher dimensions by utilizing categorified Lie 2-bialgebras and 2-graded Yang-Baxter equations to establish a zero 2-curvature condition for a 3d field theory governed by a higher derived affine Kac-Moody 2-algebra.
This paper bridges stochastic Moran processes and deterministic reaction-diffusion models by deriving partial differential equations for continuous media, revealing how distinct fitness components (fecundity vs. viability) and update rules (birth-death vs. death-birth) fundamentally alter selective wave speeds and establishing a continuous analog of isothermal graphs through local current conservation.
This paper introduces the Cavitation Acoustic Perturbation Equations (CAPE), a unified computational framework that directly embeds cavitation physics into acoustic modeling to accurately predict, localize, and analyze hydroacoustic sources and propagation in multiphase cavitating flows.
This paper demonstrates that while traversable wormholes in Unimodular Gravity and General Relativity share identical geometric and geodesic structures, they are dynamically distinguished by their source sectors, where Unimodular Gravity requires either restricted equations of state or an effective inhomogeneous vacuum contribution to sustain the same geometry.
This paper derives structurally simpler, lower-order coupled difference equations for the recurrence coefficients of orthogonal polynomials associated with oscillatory Jacobi-type weight functions, enabling their computation and the conjecture of their symbolic forms.
This paper numerically investigates random walks in a Dirichlet random environment across dimensions $d=1, 2, and 3$, verifying KPZ-like growth in lower dimensions, confirming a phase transition in , and establishing exact relationships between sample-to-sample variances and extreme diffusion coefficients.
This paper demonstrates that the physical procedure of "gauging the gauge" corresponds mathematically to categorification, generating higher-gauge theories based on crossed-modules that can resolve anomalies in quantum field theory by absorbing curvature defects.
This paper introduces a layer potential representation for solving the scattering problem in open wave-guide networks by constructing fundamental solutions via Fourier transform, reducing the transmission problem to solvable Fredholm integral equations of the second kind, and analyzing the resulting guided modes.
This paper establishes that solutions to the integral equations derived from an open wave-guide scattering model possess asymptotic expansions, which are then used to prove that the corresponding partial differential equation solutions satisfy the necessary outgoing radiation conditions.
This paper establishes the local existence of mass-conserving solutions for an inhomogeneous coagulation equation with a sedimentation transport term, demonstrating that spatial inhomogeneity prevents instantaneous gelation or non-existence phenomena observed in the corresponding spatially homogeneous models for specific classes of coagulation kernels.