3210 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 that within the generalized Korteweg--de Vries family, only the linear () and quadratic () polynomial cases satisfy the Painlevé integrability criterion and admit elliptic reductions due to integer pole orders, while all higher-degree cases () fail these structural requirements due to fractional leading exponents.
This paper proves that for a general class of laminar flows in a two-dimensional channel that behave locally like Couette flow near the boundary, the linearized Navier-Stokes operator possesses an eigenvalue that, in the large Reynolds number limit, coincides to leading order with the eigenvalue previously derived by Wasow in 1953 for pure Couette flow.
This paper proposes highly accurate spectral and spectral-element methods to efficiently compute thousands of eigenvalues for the Schrödinger operator with Robin boundary conditions on complex 2D domains, using these results to validate recent theoretical findings on Robin-to-Neumann gaps and to formulate a unified conjecture regarding their asymptotic behavior.
This paper derives the large expansion of the partition function for a two-dimensional one-component plasma on a cylinder by mapping it to an annular droplet model, revealing that unlike the annular case, the cylinder's expansion lacks a term regardless of hard wall boundary conditions.
This paper presents a comprehensive review of Seiberg-Witten theory and instanton calculus for gauge theory, demonstrating how the AGT correspondence bridges Liouville field theory and Nekrasov's partition function to reveal a topological recursion structure through classical Zamolodchikov relations.
This paper investigates two quantum spin models on -partite graphs in the thermodynamic limit, identifying three distinct magnetic phases for the spin-1/2 antiferromagnetic Heisenberg model and establishing a geometric criterion for frustration in general spin- orthogonally invariant systems.
This paper extends the analysis of gravitationally localized soliton-like solutions to the Einstein-Dirac-Higgs equations by investigating excited and many-fermion states, revealing novel stepwise Higgs field behaviors and significant ADM-to-fermion mass disparities distinct from previously studied two-fermion ground states.
This paper establishes that the optimal trace-norm relaxation rate for the one-dimensional Witten Lindbladian is given by , where is the first positive eigenvalue of the associated operator , provided the initial operators satisfy specific estimates on their Gibbs-conjugated Schwartz kernels.
This paper introduces a new family of "trickledown theorems" that utilize rank-1 perturbations of influence matrices to prove that Glauber dynamics for the Sherrington-Kirkpatrick model mixes in polynomial time for inverse temperatures up to .
This paper presents a novel construction of static, geometrically local Hamiltonians with provably volume-law entangled ground states and infinite-temperature eigenstate properties across their entire spectrum, achieved by adapting the Feynman-Kitaev clock with periodic boundary conditions and combining it with exactly solvable Floquet circuits that satisfy the eigenstate thermalization hypothesis.