2670 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 refutes the claim that a generalized de Almeida-Thouless criterion proposed by Jagannath and Tobasco universally characterizes the replica symmetric regime in mixed -spin glasses by constructing explicit counterexamples using the Hopf-Lax representation of the Parisi formula, while noting that the validity of the classical condition for the Sherrington-Kirkpatrick model remains an open question.
This note explains key elements of the recent proof by Y. Deng, Z. Hani, and X. Ma, which extends the derivation of the Boltzmann equation from hard-sphere dynamics to arbitrary large times, provided the solution remains regular, thereby overcoming the short-time limitation of Lanford's original result.
This paper establishes the convergence of solutions from a stochastic 3D Navier-Stokes system to a generalized stochastic primitive equation model that incorporates relaxed hydrostatic assumptions via martingale terms, demonstrating that this modified framework serves as a well-posed, higher-order approximation of the original equations under specific asymptotic scalings and boundary conditions.
This paper resolves a conjecture by Lawler and Werner by proving that chronologically adding loops from a Brownian loop soup to an independent radial SLE path yields a planar Brownian motion, thereby establishing a robust coupling between these processes as the scaling limit of loop-erased random walks and random walks.
This paper establishes a growth condition on the potential of a Schrödinger operator that implies Rosen inequalities for its ground state, which are then utilized to derive Logarithmic Sobolev inequalities and prove the intrinsic ultracontractivity of the associated Schrödinger semigroup.
This paper establishes the intrinsic ultracontractivity of weighted Schrödinger semigroups for a specific class of positive potentials by utilizing logarithmic Sobolev inequalities and duality arguments to prove continuous mapping between weighted and spaces.
This paper establishes a geometric framework for precontact manifolds by analyzing general pairs of 1-forms and 2-forms under mild regularity conditions, characterizing their properties, defining associated vector fields and Hamiltonian dynamics, and illustrating the theory with various examples.
This paper extends a theoretical and numerical framework for analyzing scattering on infinite plates to general two- and three-dimensional objects with compactly supported nonlinearities by transforming the full-space nonlinear Helmholtz equation into an equivalent bounded boundary-value problem using a nonlocal Dirichlet-to-Neumann operator, thereby enabling unique solutions and efficient finite element approximations.
This paper investigates the ring-theoretic and homological properties of two invariant subalgebras of rational Cherednik algebras by realizing them as rings of invariants under reductive subgroups of , thereby characterizing their centers, establishing their Cohen-Macaulay and Auslander-Gorenstein nature, and analyzing their quantum Hamiltonian reductions at parameters and .
This paper proposes a rigorous entropic-force theory demonstrating that stochasticity and discrete-time updates in neural network training generate emergent forces that break continuous symmetries to explain universal representation alignment, the Platonic Representation Hypothesis, and the reconciliation of sharpness- and flatness-seeking optimization behaviors.