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 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.
This paper utilizes the Schwarz and Jensen inequalities to derive and analyze generalized uncertainty relations for multiple non-commuting observables, demonstrating how these relations can be equivalently expressed through quantum Pearson correlation coefficients to characterize state-dependent correlations.
This paper introduces a quasi-orthogonal geometric framework for stabilizer codes that relaxes strict orthogonality constraints to enable more flexible and resource-efficient designs, demonstrating significant improvements in logical error rates and code performance under depolarizing noise compared to traditional orthogonal counterparts.
This paper provides a concise didactical introduction to quantum graphs as Schrödinger Hamiltonians on metric graphs, focusing on their role in quantum chaos and spectral theory while summarizing seminal results and recent developments in periodic orbit theory.
This paper introduces generalised (bi-)Hamiltonian structures for evolutionary partial differential equations, characterising their hydrodynamic type via geometric data and establishing their association with (bi-)flat F-manifolds and compatibility with principal hierarchies.