1668 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 derives the asymptotic first passage time distribution for space-dependent variable-order time-fractional diffusion, demonstrating that the survival probability decays as where is the minimum fractional exponent, a theoretical prediction validated by exact solutions and Monte Carlo simulations that enables the identification of spatially heterogeneous anomalous transport.
This paper constructs Lagrangian correspondences between moduli spaces of rank- Higgs bundles and holomorphic connections on a Riemann surface and specific Hilbert schemes, utilizing transversal bundles to induce divisors and parameters, thereby providing a geometric realization of the Dolbeault geometric Langlands correspondence and a pathway toward its de Rham quantization.
This paper establishes a unified framework connecting Yang-Baxter maps and the independence preserving property by demonstrating that all quadrirational Yang-Baxter maps on possess this property and that most known independence-preserving bijections can be derived from them through specific parameters or limiting procedures.
This paper extends classical spectral functionals defined via the Wodzicki residue from torsion-free Dirac operators to geometries with torsion, demonstrating that their local densities recover fundamental geometric tensors and introducing novel chiral spectral invariants through a grading operator.
This paper introduces a novel method for generating infinite sequences of quasi-isospectral higher-order Hamiltonians by reversing the conventional Lax pair interpretation to treat the higher-order -operator as the starting point, utilizing intertwining techniques to derive new integrable systems from known solutions like those of the KdV equation.
This paper derives a new class of creation-annihilation algebras for bosons and fermions by generalizing particle symmetrization through quotients of distinguishable-particle state spaces, demonstrating that these algebras reproduce the partition functions of transtatistics under specific operational principles regarding mode labeling, unitary invariance, and local particle counting.
This paper proposes using quantum linear programming algorithms to solve the optimization problems arising from dissipative measure-valued formulations of nonlinear PDEs, demonstrating potential polynomial advantages over classical methods for obtaining full Young measures in random PDEs while noting no advantage for computing their expected values.
This paper derives the translation-invariant Bogoliubov-Fröhlich Hamiltonian as the effective description for a Bose polaron system by analyzing the microscopic dynamics in the joint limit of large density and volume, subject to the constraint .
This paper reviews the application of random matrix theory to quantum chaotic systems, detailing the necessary spectral preparation, symmetry classifications (Dyson's threefold and Altland-Zirnbauer's tenfold way), statistical analysis techniques, and connections to non-linear -models, while also addressing non-Hermitian extensions for open quantum systems.
This paper utilizes pseudo-differential operators in conformal variables to analytically derive and numerically validate the criteria and normal forms for four recurrent types of modulational stability bifurcations that occur as the steepness of deep-water Stokes waves increases toward the highest wave limit.