2656 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 Fredholm determinants derived from generalized Schur measures, which represent arbitrary multiplicative statistics of Schur measures, serve as tau-functions of the 2D Toda lattice hierarchy, thereby extending previous results on finite-temperature Plancherel measures through the use of semi-infinite wedge formalism and the Boson-Fermion correspondence.
This paper establishes a theoretical link between standard differential algebra and Lie symmetry approaches to structural identifiability by introducing "parameter symmetries," proving that a parameter combination is locally structurally identifiable if and only if it is a differential invariant of these symmetries, and validating this framework through applications to biological models.
This paper establishes that Gaussian concentration inequalities are preserved under finitary codings of i.i.d. fields provided the coding volume has a finite second moment (or first moment under specific structural assumptions), thereby deriving sharp necessary and sufficient conditions for such concentration in classical lattice models like Ising and Potts systems and characterizing geometric ergodicity in one-dimensional processes.
This paper establishes a distinct structural uniqueness theorem demonstrating that, under conditions of admissible binary saturation and refinement richness, the quadratic Born rule is the sole non-negative, refinement-stable induced weight on robust record sectors within an admissible Hilbert record layer, deriving this result from bundle additivity rather than standard projector lattice additivity.
This paper analyzes the dynamic Doppler effects on electromagnetic signals observed by non-inertial receivers by deriving compact expressions for spectral and amplitude transformations induced by relativistic acceleration, jolt, and the geometric curvature and torsion of 4D Frenet-Serret spacetime paths.
This paper constructs evolutionary soliton hierarchies, including coupled Korteweg-de Vries and Harry Dym systems, by defining Novikov algebras of Stäckel type and establishing conditions for their pencils to yield centrally extended, compatible Dubrovin-Novikov Hamiltonian operators.
This paper derives exact solutions to the Schrödinger equation and continuum mechanics equations by applying a nonlinear Legendre transform to the continuity equation with a generalized Maxwell distribution as the momentum density, yielding explicit expressions for vector fields, density distributions, and potentials alongside a comprehensive physical analysis.
This paper establishes a nonperturbative framework using analytic continuation to reconstruct regular reduced dynamics from divergent time-local generators, revealing how such divergences signal the approach to noninvertibility and identifying early-time anisotropy signatures in open quantum systems like the spin-boson model.
This paper develops structure-preserving time integration schemes, including Boris-type and high-order symplectic methods, for magnetic Gaussian wave packet dynamics by reformulating the variational Dirac--Frenkel equations as a Poisson system, thereby ensuring the conservation of key invariants and providing rigorous error bounds uniform in the semiclassical parameter.
This paper presents a unified, rigorous microlocal sheaf-theoretic framework that generalizes the Maslov-WKB method to overcome caustic singularities and prove Bohr-Sommerfeld-Einstein-Brillouin-Keller quantization conditions for general semiclassical operators in one degree of freedom.