2229 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 establishes a combinatorial theory of discrete vector bundles with connection on locally ordered simplicial complexes, introducing a discrete exterior covariant derivative that mirrors smooth geometric structures and satisfies key identities like the Bianchi identity, while also linking flat connections to twisted de Rham cohomology and providing a concrete comparison with existing frameworks.
This paper presents a microscopic derivation of a -symmetric non-Hermitian sine-Gordon effective theory from a nonequilibrium spin-boson system using Keldysh functional integrals, establishing a precise dictionary between microscopic parameters and effective couplings to demonstrate that the resulting renormalization group flow, exceptional point physics, and bound-state spectrum align with established non-Hermitian sine-Gordon results.
This paper derives an effective model on a non-simply connected domain from the Ginzburg–Landau theory in a planar simply connected domain under a strong, compactly supported magnetic field, revealing oscillatory phenomena characteristic of the Little-Parks and Aharonov–Bohm effects.
This paper develops a discrete Euler-Poincaré reduction framework for mechanical systems with advected parameters and additional dynamics using group difference maps, extends the Kelvin-Noether theorem to this discrete setting, and demonstrates the method's effectiveness in preserving geometric properties through applications to underwater vehicle dynamics and numerical simulations.
This paper constructs self-catalytic branching Brownian motions with an infinite number of initial particles for the subcritical case and establishes their coming down from infinity property along with characterizing the associated convergence rates.
This paper provides a new proof extending the equivalence between weak and strong spatial mixing to a broader family of two-dimensional lattice models by introducing a "percolative picture" of information propagation.
This paper establishes that the order-disorder interface in the 2D -state Potts model (for ) at the critical temperature is a well-defined object with fluctuations that converges to a Brownian bridge under diffusive scaling, a result proven by coupling the model to the Ashkin-Teller and six-vertex models to derive a renewal picture for the interface.
This paper demonstrates that non-reciprocal higher-order interactions on m-directed hypergraphs facilitate the emergence of chimera states over a broader parameter range and enable new dynamical patterns not observed in reciprocal or pairwise systems, a finding validated through numerical simulations and phase reduction theory.
This paper establishes a general operator algebraic framework using Hilbert -modules to analyze discrete systems on interfaces, demonstrating how the essential spectrum and topological properties of such mixtures can be derived from the asymptotic behavior of their constituent bulk systems.
This paper clarifies that the Gauss-Appell principle, when applied at a fixed time to incompressible inviscid flow, yields a variational minimization that uniquely determines the reaction pressure as the Lagrange multiplier enforcing kinematic constraints, thereby recovering the Euler equations and the Leray-Hodge projection without inherently selecting global flow features like circulation.