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 introduces a new class of noncommutative algebras situated between quantum and free associative algebras, demonstrating their compatibility with the dynamics of the nonabelian Volterra hierarchy and other integrable systems like the Toda lattice and Ablowitz-Ladik system.
This paper demonstrates that while power-law velocity-dependent damping expands the set of initial data leading to global smooth solutions in one-dimensional repulsive Euler-Poisson equations, it fails to prevent finite-time blow-up for small perturbations of the steady state in multidimensional cases (except dimension 4), despite causing the amplitude of oscillations to decay.
This paper introduces and characterizes "Brownian loop-catchers," a family of random connected closed subsets that interpolate between continuum loop-erased random walks and Brownian traces for central charges , satisfying a unique recovery property where adding intersecting loops from a Brownian loop soup reconstructs the full Brownian trace.
This paper proposes an extended formulation of the first and second laws of thermodynamics that remains valid for both positive and negative absolute temperatures, thereby broadening the laws' applicability to systems such as those found in quantum cosmology and Onsager's vortices.
This paper derives degenerate addition formulas for KP hierarchy tau functions by taking limits of parameter-shifted determinants, establishing their connection to Wronskians, proving the equivalence of vertex operators and Darboux transformations, and obtaining a novel addition formula for Riemann's theta functions as a distinct limit of Fay's classical formula.
This paper proposes a two-step numerical homogenization method that decomposes a 3D heterogeneous stratified medium into 2D layers for micro-mechanical estimation and then reconstructs the global behavior using a variational sum approach to effectively capture material property gradients, as demonstrated on a thin plate with a porosity gradient.
This paper constructs path integrals for quantum dynamics on Lie groups by addressing noncommutative momentum and compact directions through winding number sums, and applies this framework to derive semiclassical approximations for Euler-Arnold systems up to two-loop order.
This paper establishes a concrete quantum-classical crossover for simulating many-body dynamics by introducing a scalable fault-tolerant framework that, under realistic error rates, outperforms state-of-the-art classical algorithms in both runtime and resource efficiency for mixed-field Ising models.
This paper presents a unified combinatorial framework that derives strong spatial mixing directly from zero-freeness using a novel Christoffel-Darboux-type identity, thereby extending Weitz's FPTAS to all known zero-free regions of general 2-spin systems with pinned vertices, including regimes where traditional tree-recurrence proofs fail.
This paper bridges information-theoretic and relativistic causality by refining causal inference techniques for unfaithful models, introducing the geometric property of conicality to distinguish space-time dimensions, and establishing a correspondence between faithful causal models and conical space-times to clarify the relationship between no-superluminal-signalling constraints and causal structures.