2563 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 proposes a differentiable framework for topology-constrained optimization that utilizes Hodge-spectral relaxations and low-pass filters to create smooth, geometry-aware surrogates for discrete homological constraints, enabling more effective optimization of Betti numbers and persistent homology in both graph and point cloud settings.
This paper constructs a discrete BF formulation of two-dimensional Carroll dilaton gravity, demonstrating that its boundary symmetries form an affine Carroll algebra with a conformal Virasoro reduction, thereby establishing the ultra-relativistic counterpart to discrete Jackiw-Teitelboim gravity.
This paper establishes a direct link between Onsager symmetry, duality defects, and quantum integrability in the XXZ spin chain at roots of unity by constructing a lattice realization of the Onsager algebra and its duality automorphism via a non-Abelian algebra of transfer matrices, thereby demonstrating that non-Abelian integrability naturally gives rise to categorical dualities and topological defect lines.
This paper demonstrates that weighted transport geometry, rather than binary topology alone, serves as the primary organizer of functional memory in complex systems, revealing a universal, low-dimensional structure where interaction strengths systematically govern memory depth across diverse biological, ecological, social, and technological networks.
This paper establishes a near-critical Ornstein--Zernike theory for the planar random-cluster model with by analyzing the renewal properties of subcritical clusters at the correlation length scale, yielding uniform asymptotic formulas for the two-point function, an invariance principle, and strict convexity of the inverse correlation length.
This paper proposes a novel, efficient method for identifying tripartite states by establishing a specific uncertainty-based criterion using non-commuting observables, which distinguishes them from other entangled states like the GHZ state without requiring complete quantum state tomography.
This paper demonstrates that time-delayed pairwise coupling in Kuramoto oscillators can be effectively recast as higher-order three-body interactions, revealing that these emergent interactions account for key dynamical features such as bistability and synchronization transitions.
This paper presents a geometrically nonlinear continuum mechanics framework for active anisotropic plates that explains how the interplay between material anisotropy, active contractility, and substrate curvature governs cell alignment patterns and structural instabilities, with applications ranging from cell biology to soft robotics.
These lecture notes from Les Houches offer a concise overview of the conceptual, computational, and mathematical foundations of tensor networks, presenting them as a powerful framework for understanding and simulating strongly correlated quantum matter by leveraging entanglement structures to overcome the many-body exponential wall.
This paper establishes a complete mathematical framework linking the entanglement of mixtures of Dicke states to convex cones of tensors, enabling the construction of explicit PPT entangled states for all multipartite systems with local dimension and providing semidefinite programming relaxations for separability testing.