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 investigates the continuum limit of the para-Bannai--Ito polynomials on a two-sided bi-lattice, demonstrating that they converge to a supersymmetric Scarf I Hamiltonian with reflections (a generalized Pöschl--Teller system) and establishing that the discrete model's perfect state transfer and lack of fractional revival are preserved in this limit.
This paper presents and validates a Direct Simulation Monte Carlo method that couples binary collision treatments with symplectic mean-field integration to model the kinetic theory of ordered fluids, successfully capturing relaxation dynamics and the isotropic-nematic phase transition for rod-like molecules.
This paper investigates two hierarchies of bivariate generating functions defined by differential recursions, revealing their connections to palindromic triangles, algebraic equations with specific Galois groups, and projective discriminants, while proposing conjectures on their algebraicity and transcendence.
This paper defines -dimensional topological quantum field theories and their lattice realizations using pivotal fusion 2-categories, introducing a -symbol formalism to prove topological invariance under 4D Pachner moves and constructing a corresponding 3D Levin-Wen-type Hamiltonian model as a higher-dimensional analogue of spin-networks.
This paper establishes that the non-compactness of the moduli space of -monopole solutions on a closed 3-manifold is equivalent to the existence of non-linear "3/2-Fueter sections," thereby providing a Haydys-type correspondence for -spinors and analyzing the non-elliptic nature of the associated Fueter operator through a generalized Rarita-Schwinger framework.
This paper establishes a generalized area law for gapped ground states of fully connected (geometrically non-local) Hamiltonians, demonstrating that their bipartite entanglement entropy grows at most logarithmically with system size, thereby enabling efficient matrix product state approximations and polylogarithmic-time computation for permutation-invariant cases.
This paper rigorously proves the entanglement area law for one-dimensional interacting boson systems with long-range interactions, including Bose-Hubbard and models, by introducing a general Hilbert space dimension reduction method that ensures efficient Matrix-Product-State approximations for ground states.
This paper establishes a connection between graph complexes, Calabi-Yau -categories, and Kontsevich's cocycle construction by producing a commutative square of shifted Poisson algebras that generalizes the Loday-Quillen-Tsygan map and admits a quantized version via Beilinson-Drinfeld algebras, thereby offering categorical methods to relate enumerative geometry and large gauge theories.
This paper constructs an open-closed formality morphism dependent on a non-commutative Hodge filtration splitting, which serves as a crucial ingredient for quantizing large open string field theory and conjecturally provides an algebraic framework for open-closed Gromov-Witten invariants.
This paper investigates a unitary deformation of the phase evolution generator that introduces logarithmic spectral curvature without causing decoherence, proposing a spectroscopy protocol to distinguish this specific nonlinear signature from other anharmonicities by analyzing second and higher spectral differences across multiple energy levels.