1515 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 Yang-Mills theory coupled to a particle on a cylinder reduces to a finite-dimensional quantum system, yielding a Landau problem on a torus for the Abelian case and a one-dimensional Calogero-Sutherland-type many-body system for the non-Abelian SU(N) case.
This paper establishes conditions involving manifold curvature, inverse temperature, and escaping directions from saddle points that guarantee polynomial mixing times for Langevin dynamics to Gibbs measures on Riemannian manifolds, thereby avoiding barren plateaus and spurious local minima through a novel relation between processes in the domain and their Riemannian submersion images.
This paper investigates the stochastic population dynamics of surface-mediated autocatalytic processes where particles diffuse and undergo competing replication or death events, providing a systematic theoretical analysis of the population's statistical properties across vanishing, steady-state, and exponential growth regimes supported by numerical solutions and Monte Carlo simulations.
This paper introduces "Quantum Logic Codes," a family of high-rate stabilizer quantum error-correcting codes constructed from small base codes via tiling and concatenation that provably support a constant-depth, complete transversal logical Clifford instruction set architecture, including novel depth-one implementations of and gates.
This paper generalizes the ZX calculus to two-dimensional Yang-Mills theory with a compact gauge group by leveraging a shared Hopf Frobenius algebraic structure, thereby establishing a foundation for applying this graphical formalism to low-dimensional gravity.
This paper introduces a graphical coaction framework for Friedmann-Robertson-Walker (FRW) integrals at all loop orders using intersection theory in twisted (co)homology to decompose cosmological observables into graph-based building blocks, thereby revealing the combinatorial structure of their governing differential equations and providing open-source tools for their computation.
This paper advances the open topological string/spectral theory correspondence by constructing entire, off-shell eigenfunctions for quantized mirror curves from open topological string partition functions, specifically applying this framework to local to derive eigenfunctions for the modified Mathieu and McCoy-Tracy-Wu operators and uncovering a functional relation between them.
This paper utilizes the path integral formalism and an approximation for the centrifugal term to derive the energy spectrum and wave functions for a linear combination of Yukawa and four-parameter diatomic potentials, subsequently using these results to calculate the system's partition function and thermodynamic properties.
This paper systematically unifies different notions of higher Hilbert spaces and their associated module categories by introducing -dagger categories and -Hermitian 2-vector spaces, where varying subgroups recover distinct operator algebra structures like , , and -algebras, while also proposing criteria for positivity and an inductive framework for arbitrary dimensions.
This paper presents numerical simulations of static equilibrium configurations for a flat hyperelastic body embedded in a curved surface of revolution, demonstrating how the interplay between curvature-induced restorative forces and gravitational potential can create a "levitation" phenomenon where the body's deformation forces perfectly cancel gravitational pull.