2548 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 establishes a Central Limit Theorem for non-linear functionals of discrete Gaussian fields on the -dimensional lattice using Wiener chaos decomposition and the fourth moment theorem, demonstrating that even powers of the discrete Gaussian Free Field converge to Gaussian white noise while odd powers converge to a continuous Gaussian Free Field with explicit covariance.
This review categorizes the various ways octonions and split-octonions have been used to formulate the Dirac equation into four distinct approaches, clarifies the historical origins of the 2-factor method, and demonstrates that a recent "novel" split-octonionic formulation is mathematically equivalent to an existing direct-product representation.
This paper establishes a geometric correspondence between the Lorentzian Raychaudhuri equation and Perelman's Ricci flow non-collapsing theorem to derive a Lorentzian non-collapsing result, introduce a covariant entropy functional for causal volume, and propose a "geodesic entropy capacity" that unifies gravitation, thermodynamics, and information theory.
This paper establishes deep connections between electrical networks, Grassmannians, and cluster algebras by constructing a specific seed in Scott's cluster algebra on to relate circular total positivity to Grassmannian positivity, and by proving that the Laurent Phenomenon algebra is isomorphic to the coordinate ring of the space of electrical networks.
This paper proposes a unified entropic framework for real fluids that utilizes Geometrothermodynamics to link macroscopic critical phenomena and intermolecular force balances to the scalar curvature of the equilibrium manifold, while introducing universal dimensionless ratios and Bayesian statistical methods to characterize and validate the geometric scaling behavior across different equations of state.
This paper proves that the suitably centered and rescaled Green's function of the weakly coupled four-dimensional Anderson model with spatial white noise converges to a centered Gaussian random field by developing a multiscale analysis with truncated renormalized parametrix to handle the factorial complexity of high-order renormalization terms.
This paper investigates Krylov spread complexity for time-dependent quantum systems by formulating the problem within Floquet theory for periodic driving and extending the framework to general time-dependent cases using both globally and piecewise truncated Magnus expansions to ensure reliable analysis when standard expansions fail.
This paper establishes the global existence and optimal large-time decay rates for weak and strong solutions of a three-dimensional penalized Navier--Stokes system featuring biharmonic damping and a Temam-type correction, while proving that all derived a priori estimates remain uniform with respect to the penalization parameter.
This paper proposes a delay-free, higher-order approximation framework for the time-delayed Kuramoto model that, through analytical reduction and numerical validation, enables more accurate prediction of collective dynamics and the control of complex states like bistability and intermediate synchronization compared to conventional pairwise approaches.
This paper proves that Lee-Yang Hamiltonians under a uniform Z-field possess a spectral gap of at least h/4 independent of system size and coupling strengths, a result derived from partition function zero-freeness that enables a polynomial-time quantum algorithm for computing their ground state energy.