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 establishes that the existence of purely electric or purely magnetic Weyl curvature tensors on compact -dimensional manifolds is obstructed by the vanishing of specific products of Pontryagin classes in the top-degree de Rham cohomology, thereby providing nontrivial topological constraints on such Lorentzian metrics and their associated Petrov subtypes.
This paper extends the Kuramoto-Sakaguchi model to general Riemannian manifolds to demonstrate that while geometry determines the critical coupling for synchronization, topology (specifically the Euler characteristic) fundamentally constrains the nature of the phase transition, permitting continuous or tricritical transitions only on manifolds with zero Euler characteristic.
This paper establishes a categorical and algebro-geometric framework for localization in cohomological theories with open-closed recollements, demonstrating that natural outputs are torsors of supported refinements rather than distinguished classes, and showing how imposing uniqueness or concentration principles recovers familiar index formulas and unifies various localization techniques like Atiyah-Bott-Berline-Vergne and Lefschetz decompositions.
This thesis provides a comprehensive and clarified derivation of analytical solutions to the Ornstein-Zernike integral equation for hard-sphere and charged hard-sphere systems under the Percus-Yevick and Mean Spherical Approximations, utilizing advanced mathematical techniques to rigorously establish macroscopic thermodynamic properties.
This paper investigates the disorder-free Sachdev-Ye-Kitaev (SYK) model and finds that, unlike the Fréchet distributions observed in the Lieb-Liniger model, the off-diagonal matrix elements of operators composed of four or more Majorana fermions are well-described by a generalized inverse Gaussian distribution.
This paper proposes a data-driven boundary control framework for Distributed Port-Hamiltonian systems that combines Gaussian Process learning to infer unknown Hamiltonian structures with energy-based robustness analysis, ensuring probabilistic boundedness of closed-loop trajectories despite model mismatches.
This paper establishes that reduced-order models for phononic, acoustic, and photonic band structure computations achieve exponential convergence rates determined by spectral gaps, as proven via Kolmogorov -width analysis of holomorphic eigenpairs and spectral projectors, thereby providing a sharp optimality benchmark that validates the effectiveness of greedy algorithms and existing methods like RBME.
This paper proves that univariate hyperbolic beta integrals and conical functions degenerate into two-dimensional integrals over the complex plane by establishing uniform bounds on their integrands.
This paper proposes a program to bridge perturbative BV-BFV quantization of Chern-Simons theory with non-perturbative Reshetikhin-Turaev invariants by conjecturing their equivalence as extended topological quantum field theories, mediated by factorization homology, derived character stacks, and -Koszul duality.
This paper introduces a qubit-efficient quantum encoding for the capacitated vehicle routing problem using a global-position colored-permutation framework that eliminates the need for explicit load registers, thereby reducing logical qubit overhead while maintaining strong algorithmic performance and recovering verified optima on standard benchmarks.