1605 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 proposes the Energy-Projection Fourier Neural Operator (EP-FNO), a structure-informed architecture that integrates invariant projection with residual FNO updates to significantly enhance long-time stability and accuracy in predicting parametric Hamiltonian PDEs by preserving conserved quantities and reducing phase errors.
This paper derives how noninertial motion, characterized by proper acceleration, jerk, and higher-order geometric invariants, induces unique nonlinear amplitude and phase modifications in Dirac spinor fields that distinguish them from scalar fields through observable spin-dependent dynamic Doppler signatures.
This paper establishes a unified bulk-first framework deriving both ordinary and generalized Schwarzian dynamics from two-dimensional BF gravity via Drinfeld-Sokolov reductions, revealing how higher-rank sl(3,R) theories governed by Wilczynski invariants naturally link flat BF connections to projective geometry, Casimir charges, and boundary thermodynamics.
This paper establishes a generalized, substrate-independent formal definition of assembly spaces and indices while introducing efficient grammar-based algorithms to approximate these metrics, thereby providing a unified framework to advance the detection of life signatures across chemistry, biology, and complexity science.
This paper applies Lie symmetry analysis and conservation-law theory to the Jaynes-Cummings model, revealing new invariant solutions involving Heun polynomials and deriving a hierarchy of conservation laws that link atomic purity, coherence, and entanglement dynamics to the system's symmetry structure.
This paper presents and analyzes a high-order Nyström method for solving the coupled boundary integral equations arising in oblique-incidence electromagnetic scattering by impedance cylinders, demonstrating its stability, accuracy, and effectiveness through rigorous theoretical convergence analysis and comprehensive numerical experiments.
This paper employs the nonlinear steepest descent method on a Riemann-Hilbert problem to derive the long-time asymptotic expansion of the defocusing mKdV equation with step-like initial data in transition regions, revealing that the subleading term decays as with a coefficient determined by the Painlevé XXXIV model.
This paper investigates a non-Hermitian matrix model that interpolates between ensembles obeying the Single Ring Theorem and normal matrices, revealing that the theorem's breakdown occurs early in the flow while singular value statistics transition from Wigner-Dyson to Poissonian, and proposing a conjecture to reconstruct eigenvalue densities from singular values using random permutations.
This paper investigates the energy spectrum of a quantum vortex ring in a flowing fluid within a cylindrical pipe, demonstrating the existence of states with negative and large effective masses, proposing a mechanism for turbulence formation based on coupled vortex pairs, and offering a new method to determine the critical Reynolds number in quantum turbulence.
This paper establishes that the generalized Stieltjes system defined by a monic polynomial source of degree possesses exactly solutions for generic parameters, a bound derived from intersection multiplicity that is attained on a Zariski open set, while also characterizing the asymptotic behavior of these solutions as the system decomposes into weakly coupled classical Stieltjes systems near the zeros of the source polynomial.