3383 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 demonstrates that the Zassenhaus formula simplifies under the "no-mixed adjoint property," enabling an exact, Trotterization-free Unitary Coupled Cluster ansatz for strongly correlated electron systems that requires only a finite number of Givens gates and clarifies the conditions for exact solutions in disentangled forms.
This paper demonstrates that interacting paraparticle chains with flavor-blind Hamiltonians exhibit a factorized Hilbert space where periodic boundary conditions induce flux sectors that render parastatistics observable as shifted conformal towers in the energy spectrum, effectively mapping the system to an exactly solvable XXZ chain with flux.
This paper establishes the unique identifiability of drift and diffusion terms in nonlinear stochastic differential equations by analyzing their ergodic invariant measures, thereby transforming the inverse problem into a uniqueness question for stationary Fokker-Planck equations and revealing fundamental distinctions between drift and diffusion recovery.
This paper investigates a generalized two-dimensional nonlinear Schrödinger equation with arbitrary potential and dispersion functions, deriving various dimensional reductions and presenting numerous new exact solutions through methods like functional separation of variables and structural analogy to serve as benchmarks for numerical and analytical verification.
This paper introduces a novel, verified algorithm that leverages spectral graph theory and vertex curvatures to efficiently and accurately determine graph isomorphism in polynomial time, successfully resolving challenging instances that defeat classical spectral techniques.
This paper unifies three major categories of mathematical results on quiescent big bang singularities by demonstrating that solutions satisfying recent general conditions for big bang formation indeed induce well-defined initial data on the singularity, thereby bridging the gap between stable formation proofs and geometric data construction.
This paper establishes a functorial framework ensuring the convergence, continuity, and holomorphic dependence of Drinfeld's Universal Deformation Formula on spaces of analytic vectors by matching series order with equicontinuity conditions, thereby affirmatively resolving Giaquinto and Zhang's question regarding the existence of strict versions for their explicit twists.
This paper introduces and analyzes the novel mathematical concept of "dynamic level sets," which arises from a 2012 Turing incomputability study and relies on the Principle of Self-Modifiability to explain how physical reconfiguration via incomputable processes can generate computational behaviors distinct from standard dynamical systems and probabilistic Turing machines.
This paper extends Remling's Theorem to vector-valued discrete Schrödinger operators by demonstrating that the -limit points of their matrix potentials are reflectionless on the absolutely continuous spectrum with full multiplicity under the shift map.
This paper investigates the Hankel determinant associated with a perturbed Laguerre weight featuring pole singularities of order up to two, deriving a system of difference equations for recurrence coefficients and establishing coupled partial differential equations that reduce to generalized Painlevé III' equations, while also extending the analysis to higher-order pole perturbations.