3307 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 the essential spectrum of the non-Abelian covariant Laplacian on remains if the curvature decays faster than , while demonstrating that this threshold is sharp by constructing a smooth connection with decay where zero enters the essential spectrum.
This paper utilizes the open topological string/spectral theory correspondence to construct exact, analytic generalized eigenfunctions for a class of finite-difference Schrödinger operators arising from supersymmetric Yang-Mills theory, providing a rare example of an exactly solvable spectral problem that describes both bound and resonant states across arbitrary polynomial potentials.
This paper establishes a comprehensive framework for characterizing quantum resources in SU(1,1) systems by constructing covariant quasiprobability distributions on the Poincaré disk, demonstrating that Wigner negativity serves as a definitive witness of nonclassicality for these states, and introducing stellar rank and generalized multipoles as complementary tools for quantifying quantumness.
This paper rigorously derives the measure on the two-dimensional torus as the limit of many-body quantum Gibbs states with general symmetric -body interactions by employing a graphical formalism to systematically organize Wick renormalization-induced lower-order terms and utilizing a uniform logarithmic stability estimate to control these terms via the leading interaction's positivity.
This paper introduces a three-term recurrence relation that efficiently generates explicit higher-order rational rogue wave solutions for the nonlinear Schrödinger equation using smaller determinants, thereby enabling the derivation of seventh-order waves with six arbitrary complex parameters to explore new wave patterns.
This paper introduces the first interactive web platform that unifies the construction of Feynman ribbon diagrams, the tensor-network evaluation of higher-rank Chern--Simons knot invariants, and the identification of corresponding arborescent (FRD-like) knots within a single visual workflow.
This paper establishes new de Finetti theorems for quantum states constrained to be fixed points of quantum channels by combining mean-ergodic theorems with conditional expectation theory to derive tight capacity bounds, refined convergence rates, and polynomial-time rounding schemes for separability problems under symmetry constraints.
This paper establishes that continuous data assimilation for the two-dimensional Navier-Stokes equations with Navier-slip boundary conditions can achieve exponential synchronization using only finite-dimensional tangential velocity measurements on a boundary subset, provided the feedback strength and observation resolution are sufficient to generate a coercive spectral gap.
This paper establishes a Dirac deformation theory that interpolates between twisted Dirac and Poisson geometries, proving its compatibility with fundamental structural operations and demonstrating its power to uniformly recover diverse deformation phenomena ranging from quasi-Hamiltonian to Hamiltonian reduction and the transition from multiplicative to additive geometric structures.
This paper establishes a new, significantly improved upper bound of order on the satisfiability threshold for random quantum -SAT by combining a geometric formulation with dimension-decay analysis and a multiplicative Shearer-type inequality for tensor-product subspaces.