2619 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 investigates the relationship between the generalized i-boson model and boxed BUC plane partitions by analyzing algebraic representations and vertex operators to derive a generating function expressed as products of Schur Q-functions and explore its double scaling limit.
This paper develops a general abstract theory for continuous data assimilation of semilinear parabolic equations under multiplicative observation noise within a Gelfand triple framework, proving mean square and almost sure convergence of the assimilation error and demonstrating its applicability to various PDE models including Navier-Stokes and Allen-Cahn equations.
This paper demonstrates that Hamiltonians with real-valued eigenfunctions, constructed via Laplacians on metric graphs undergoing topology changes, can exhibit non-trivial geometric Berry's phase, thereby establishing a connection between such phases and topological transitions.
This paper presents a novel derivation of the overdamped limit for kinetic Langevin dynamics with position-dependent coefficients using -hypocoercivity, which clarifies the origin of noise-induced drift, extends to coarse-grained and variable-mass models relevant to computational chemistry, and corrects an error in related literature.
This paper establishes an operator-theoretic foundation for nonextensive statistical mechanics by demonstrating that a variational framework based on a self-referential nonlinear operator naturally yields Tsallis statistics in the mean-field limit, with the entropic index emerging directly from the operator's structural exponents rather than being postulated.
This paper reviews the construction of trial states for the dilute Bose gas using a local particle number cutoff to capture ground state correlations and provides a simplified derivation of the Lee-Huang-Yang correction as an upper bound for the ground state energy.
This paper establishes a volume-uniform spectral stability theorem for energy-truncated effective Hamiltonians in bounded finite-range quantum spin systems, proving that low-energy spectral subspaces remain stable with exponentially small errors in both finite and infinite volumes, thereby extending previous finite-volume results to the thermodynamic limit.
This paper mathematically proves the modularity of the two-dimensional conformal traintrack integral by demonstrating that its associated Picard-Fuchs system factorizes into a tensor product of Gauss hypergeometric systems through a specific gauge transformation.
Motivated by problems in conformal field theory and Narain moduli spaces, this paper classifies the minimizers and maximizers of ratios and differences of theta and Epstein zeta functions, demonstrating that the hexagonal lattice plays a pivotal role in these optimization problems with applications to crystallization and interacting particle theory.
This paper investigates the hydrodynamic behavior of the -species particle-exchange process, deriving explicit solutions for its coupled inviscid Burgers equations and characterizing the stationary phase diagram of the open system, which exhibits boundary-induced phases analogous to the single-species asymmetric simple exclusion process.