1695 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 develops an operator approach for integrating linear differential equations based on intertwining relations, demonstrating that the problem reduces to Riccati-type equations in low-order cases and enabling the construction of solutions for linear partial differential equations, such as the Klein–Gordon equation.
This paper establishes a robust bulk-boundary correspondence for two-dimensional non-Hermitian systems by utilizing Toeplitz operators and singular values instead of eigenvalues, thereby providing a stable topological classification for edge and corner modes that remains valid even under perturbations that break translational symmetry.
This paper presents a fully discrete, non-perturbative BF formulation of Jackiw-Teitelboim gravity that derives boundary symmetries, quantization, and Bekenstein-Hawking entropy directly from lattice holonomies and dilatons, thereby reproducing continuum results without relying on a fundamental Schwarzian action.
This paper revisits the one-body problem in open quantum systems to demonstrate how non-Hermiticity arises from infinite environments, unifies two definitions of resonant states to construct a new complete basis set, and applies this framework to analyze non-Markovian dynamics and time-reversal symmetry.
This paper proposes an experimentally feasible scheme using a coherent feedback loop and coherent driving field to significantly enhance the simultaneous quantum estimation precision of photon-magnon and magnon-mechanical coupling strengths in a hybrid cavity magnomechanical system, demonstrating that the right logarithmic derivative bound offers superior performance over the symmetric logarithmic derivative bound and that heterodyne detection can closely approach these ultimate quantum limits.
This paper establishes sharp rigidity and characterization results for complete spacelike linear Weingarten submanifolds with parallel normalized mean curvature and flat normal bundle in locally symmetric semi-Riemannian spaces by employing a Simons-type formula and the Cheng-Yau modified operator under various curvature and analytic conditions.
This paper presents a short-time expansion method for one-dimensional Fokker-Planck equations with spatially dependent diffusion coefficients across general stochastic integral discretization parameters, decomposing the propagator into a closed-form singular term and a regular term computable via a Taylor series with coefficients satisfying ordinary differential equations.
This paper constructs exactly solvable commuting-projector Hamiltonian models for non-chiral 2+1D fermionic symmetry-enriched topological phases, including those with specific 't Hooft anomalies, by defining -graded super fusion categories and characterizing anomalies through violations of fermion-parity conservation in surface -moves and a new obstruction in the pentagon equation.
This paper establishes a p-adic version of the Ghobber-Jaming uncertainty principle for finite-dimensional p-adic Hilbert spaces and extends the result to non-Archimedean Banach spaces by deriving an inequality that bounds the norm of a vector based on its maximum coefficients relative to two orthonormal bases.
This paper proposes a mechanism for controlling magnetic Skyrmion motion by inducing a Skyrmion number current through the anisotropic breathing mode generated by circularly polarized light, offering a low-dissipation alternative to electric currents for efficient Skyrmion manipulation.