1647 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 an exact mapping between finite-temperature homological quantum codes and a -dimensional spacetime polymer gas with topological charges, utilizing this reformulation to derive rigorous low-temperature stability criteria, exact higher-form dualities, and connections to the plaquette random-cluster model.
This paper reformulates phonons in crystalline solids by identifying the translational order parameter as a section of an associated torus bundle, utilizing a canonical flat Ehresmann connection to define a globally covariant displacement gradient that recovers standard linear elasticity and acoustic phonon spectra locally while providing a rigorous geometric framework for both symmorphic and nonsymmorphic crystals.
This paper introduces a thermodynamically consistent metriplectic dynamical system on the one-jet bundle that preserves the Hamiltonian while monotonically increasing the entropy, demonstrating its utility by deriving the Duffing equation as a subsystem amenable to asymptotic stability analysis.
This paper introduces the moduli space of metric Möbius graphs to unify the study of Riemann and Klein surfaces, deriving refined lattice point counting recursions and explicit Euler characteristics that answer a longstanding question posed by Goulden, Harer, and Jackson.
This paper establishes a framework for symmetry actions on hidden quantum Markov models (HQMMs) in one-dimensional quantum spin systems, demonstrating that such models naturally classify symmetry-protected topological (SPT) phases via group-cohomology 2-cocycles and successfully reproducing the SPT properties of the AKLT chain through a stochastic, Markovian description of virtual dynamics.
This paper employs quantum field theoretical methods to compute the joint distributions of arbitrary numbers of eigenvectors for real and complex symmetric random tensors, deriving their random matrix representations and large-dimension asymptotics to demonstrate a universal behavior across tensor geometries that extends previous findings on mean distributions.
This paper introduces two-parameter classes of exactly solvable quantum systems characterized by tridiagonal Hamiltonians and wavefunctions expanded in orthogonal polynomials, demonstrating that specific parameter thresholds can induce bound states or resonances even in systems with purely continuous spectra, despite the inability to derive their potential functions analytically.
This paper constructs families of periodic planar lattices, specifically Apollonian lattices, that achieve arbitrarily high critical temperatures for the ferromagnetic Ising model by demonstrating that scales logarithmically with the maximal coordination number and conjecturing this family to be optimal for such systems.
This paper investigates the relationship between the generalized i-boson model and boxed BUC plane partitions by analyzing algebraic representations and vertex operators to derive a generating function expressed as products of Schur Q-functions and explore its double scaling limit.
This paper develops a general abstract theory for continuous data assimilation of semilinear parabolic equations under multiplicative observation noise within a Gelfand triple framework, proving mean square and almost sure convergence of the assimilation error and demonstrating its applicability to various PDE models including Navier-Stokes and Allen-Cahn equations.