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 establishes lower comparison bounds and regularity properties for disorder-averaged ferromagnetic XY models by leveraging Ginibre's inequality and Jensen-type arguments to analyze the effects of random couplings and site dilution on phase transitions and susceptibility thresholds in two dimensions.
This paper introduces a novel graph invariant derived from the Pauli-support sets of local Hamiltonian neighborhoods, proving its invariance for periodic graphs and extending its framework to aperiodic structures like quasicrystals to provide a new operator-theoretic mechanism for comparing graph-based quantum systems.
This paper addresses the need for efficient and precise calculations of inductive coupling in large arrays of wire ring resonators under non-quasistatic conditions by deriving a series expansion for generalized inductance and proposing a numerical approximation method validated through examples of loop pairs and metamaterial scattering.
This paper refutes Aaronson's conjecture that Schrödinger's hidden-variable theory is robust against small perturbations by constructing a counterexample, while simultaneously proposing a modified version of the theory that satisfies robustness and all other desirable axioms.
This paper derives a canonical Lagrangian formulation for the two-dimensional Lotka-Volterra predator-prey system directly from its Hamiltonian, revealing a mechanical interpretation of the dynamics as a particle in a potential well with position-dependent damping or "revving," and verifies the construction by identifying the system's Hamiltonian as the conserved quantity via Noether's theorem.
This paper introduces discrete -Frobenius algebras as categorical tools to construct infinite-index Möbius covariant extensions of quantum field theories, demonstrating that commutative algebras yield local extensions while non-commutative ones generate distinct non-local extensions generated by left and right charged fields.
This paper explicitly derives connection formulas for the asymptotic solutions of a system of coupled Painlevé-II equations with symmetry-breaking parameters by employing an asymptotically exact WKB approach based on the quantum-mechanical independent crossing approximation for a time-dependent Schrödinger equation.
This paper proposes a hybridized staggered discontinuous Galerkin--mixed finite element method for strain gradient elasticity that achieves parameter-robust stability and optimal convergence by recasting the fourth-order problem into a first-order system with strong symmetry enforcement and a hybridized formulation that minimizes global coupling.
This paper establishes a theoretical framework using the Lippmann-Schwinger formulation to characterize subwavelength exceptional points in dispersive resonator arrays as defective characteristic values of a nonlinear matrix pencil, demonstrating that passive damping and detuning can induce these degeneracies and deriving explicit conditions for their inverse design and enhanced spectral sensitivity.
This paper proposes and validates a variational, quasi-static mathematical model for irreversible collagen damage in anisotropic myocardial tissue, demonstrating that post-infarction load redistribution within the left ventricle drives passive, dissipative damage consistent with experimental observations.