3210 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 generalizes the concept of symmetry defects from onsite to matrix product unitary (MPU) symmetries in matrix product states, establishing a framework to gauge these symmetries either by promoting defects to commuting gauge constraints under block independence or via a "state-level gauging" method that yields non-commuting constraints when the symmetry is anomalous.
This paper introduces a Z2 energy-resolved topological marker based on matrix homotopy and position-space descriptions to classify fragile topology in finite, disordered, and aperiodic systems, demonstrating its robustness and applicability in models like twisted bilayer graphene and photonic crystals.
This paper investigates the emergence of complexity in Radon transforms, particularly when dealing with pure-real functions, by analyzing singular points via the Fourier slice theorem and proposing methods such as hybrid Wigner-like functions to naturally introduce this complexity, thereby enhancing reconstruction and optimization procedures for ill-posed inverse problems.
This paper establishes precise large asymptotic expansions for the moment generating function of random polynomials formed by eigenvalue moduli of random normal matrices, confirming a conjecture by Byun and Charlier and providing the first free energy expansion for two-dimensional Coulomb gases with circular root- and jump-type singularities.
This paper introduces a minimal model and employs stochastic density functional theory to demonstrate how memory-coupled trail interactions fundamentally reshape collective dynamics, leading to superdiffusive spreading and transient clustering in repulsive systems or finite-time condensation into frozen states in attractive ones.
This paper presents an exact analytical solution for wave scattering by a transversal defect in a discrete square-lattice waveguide using the pole removal technique, achieving high-precision results that validate both continuous waveguide theory and numerical simulations.
This paper establishes a framework for characterizing the infrared phases of 3D fermionic theories with finite symmetries by classifying quantum anomalies into two distinct classes: those that permit symmetric gapped states and those that enforce symmetry-preserving gaplessness, thereby providing concrete predictions for candidate IR phases in (3+1)-dimensional gauge theories.
This paper establishes that the path dependence and non-autonomy of coarse-grained dynamical systems arise from missing state information, providing a constructive framework to recover the minimal number of auxiliary variables required for exact autonomous evolution via memory kernel analysis, Hankel rank determination, and Ho–Kalman factorization.
This paper establishes a rigorous energy formulation and diffusive representation for linear anisotropic fractional Maxwell–Cole–Cole media, demonstrating that fractional polarization power decomposes into nonnegative storage and dissipation components to prove electromagnetic passivity, global energy decay, and uniqueness while characterizing the broadened dielectric-loss bands and integrable initial layers inherent to fractional-order relaxation.
SIREN is a nonlinear Rankine-source boundary element solver that improves upon traditional methods by using an iteratively updated Neumann problem with a rigid-lid free surface and dynamic wet/dry panel marking to accurately compute the steady wave resistance of marine vehicles in calm water.