2548 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 proves that the logarithmic growth of phase-uniform dynamical bounds and their dependence on moment order are sharp for a class of one-frequency quasiperiodic Schrödinger operators with even potentials, utilizing a reflective version of semi-uniformly localized eigenfunctions to establish matching lower bounds.
This paper establishes a systematic framework for the critical cohomology of quasimap moduli spaces to Nakajima quiver varieties by presenting them as global critical loci, thereby constructing compatible actions of shifted Yangians and quantized Coulomb branches and proposing a geometric morphism between their associated algebras.
This paper establishes a positive mass theorem and its rigidity counterpart for a specific class of asymptotically flat metrics on the tangent bundle of an asymptotically flat manifold, demonstrating that their generalized mass is well-defined and determined by the geometry of the base manifold despite decaying below the standard ADM threshold.
This paper introduces ENPINN, an energy-norm-guided gradient-enhanced physics-informed neural network that systematically incorporates variational structure and modified residual derivatives into the loss function to theoretically and numerically overcome the limitations of existing PINN variants in accurately resolving sharp gradients and boundary layers in generalized transport problems.
This paper establishes a general bulk-edge correspondence for strong topological insulators with arbitrary curved boundaries by utilizing Roe algebras and non-separable KK-theory to prove the equivalence of various topological invariants, including Fredholm index pairings and generalized Kubo formulas.
This paper proposes and analyzes a time-modulated refocusing technique for inhomogeneous, dissipative media that utilizes a normalized directional energy estimate to design a modulation profile which cancels geometric distortion and equalizes directional attenuation, thereby achieving a coherent, high-fidelity point focus at the source location without requiring a complete model of the medium's losses.
This paper rigorously derives the cubic-quintic nonlinear Schrödinger functional as the mean-field limit for a one-dimensional homogeneous Bose gas with attractive two-body and repulsive three-body interactions, specifically analyzing how the repulsive three-body term influences ground state energy and mass concentration.
This paper rigorously derives the homogeneous cubic-quintic nonlinear Schrödinger functional as the mean-field limit for a two-dimensional Bose gas with attractive two-body and repulsive three-body interactions, analyzing the system's behavior through Hartree theory.
This paper investigates the existence of minimizers and derives effective Thomas-Fermi-like models for a homogeneous Bose gas in low dimensions () featuring attractive two-body and repulsive three-body interactions, specifically analyzing the system's behavior in the limit of a large effective statistics parameter.
This paper evaluates the capability of Quantum Physics-Informed Neural Networks (QPINNs) to solve the Korteweg-de Vries equation for multiple wave propagation in weakly nonlinear media, using high-genus analytical solutions as a rigorous testbed to assess the technology's maturity for complex evolutionary partial differential equations.