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 demonstrates that tropicalizing scalar quantum field theory yields an exact, non-linear recursion solution for the quantum effective action that enables a polynomial-time algorithm to sample moduli spaces of metric graphs, thereby proving that perturbative QFT computations lie in the polynomial-time complexity class and successfully evaluating the beta function at 50 loops.
This paper introduces ff-bifbox, an open-source, scalable toolbox that integrates FreeFEM and PETSc to perform numerical branch tracing, stability analysis, and time integration for large, time-dependent nonlinear PDEs on adaptively refined 2D and 3D meshes, validated through novel results on the Brusselator, plate buckling, and compressible Navier-Stokes systems.
This paper introduces a unified framework and modular algorithm that overcomes the mathematical challenges of infinite-dimensional state spaces and unbounded Hamiltonians to learn external potentials, such as Coulomb and periodic interactions, using free-fermion models in continuous space.
This paper rigorously characterizes the tail probability of rogue wave formation in 2D pure gravity deep water waves by proving that they most likely arise through dispersive focusing over optimal timescales, utilizing a novel method that combines normal forms and probabilistic techniques to propagate statistical information without requiring Gaussian approximations.
This paper establishes an exact 1D-2D correspondence for 2D fermions in a rotating trap (generalizing the Lowest Landau Level problem), enabling a simplified 1D quantum mechanical description of the system's density and entanglement entropy while revealing unique noncommutative features such as the absence of logarithmic scaling in the latter.
This paper presents two methodical observations in hyperkähler geometry: a simple explicit proof of a necessary and sufficient condition for a Kähler manifold to be hyperkähler, and a clarification of the two-stage Kähler reduction process (with the second stage identified as Hamiltonian reduction) illustrated through toy models reducing to and to the Taub-NUT metric.
This paper establishes a Hirota-tau and Heun-function framework for a modified affine Toda model to demonstrate that fermion-soliton interactions, governed by one-loop quantum corrections and a deformed Noether-topological current, yield stable kink configurations with a complete scattering spectrum that has implications for topologically protected states in quantum and condensed-matter systems.
This paper demonstrates that a generalized quantum theory framework connects to Liénard and Levinson-Smith nonlinear systems, yielding closed-form solutions for the former via Abel conversion and revealing solitonic-like solutions and position-dependent mass relevance for the latter.
This paper proposes a minimally structured Neural Ordinary Differential Equation architecture that enforces trajectory stability and parameterizes multistable nonlinear systems by learning a vector field with a contraction term and an implicit equilibrium map, enabling efficient data-driven discovery and gradient-based control.
This paper establishes a one-to-one correspondence between the shape resonances of two-dimensional magnetic Stark Hamiltonians with potential wells and the discrete eigenvalues of a reference operator in the semiclassical limit, thereby deriving the Weyl law for resonance counts and characterizing their asymptotic behavior near potential well bottoms.