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 proves the Simó-Yoccoz conjecture by demonstrating that for any set of four positive masses and any cyclic ordering, there exists exactly one strictly convex planar central configuration up to similarity, utilizing a uniform Hessian bound, interval arithmetic, and formal verification in the Lean proof assistant.
This paper introduces a multilevel normalizing-flow sampler that operates directly in plaquette space by employing a coarse-to-fine factorization to exactly satisfy local Bianchi constraints, thereby overcoming the learning challenges of long-range correlations in link-space models and significantly outperforming traditional methods, particularly in the weak-coupling regime.
This paper characterizes the non-equilibrium steady state of the open symmetric exclusion process on a connected graph with reservoirs as a convex combination of product Bernoulli measures, where the mixing weights are determined by the absorption probabilities of a dual stochastic process and explicitly computed for homogeneous segments.
This paper proposes a quantum mechanical scattering model with a unitary S-matrix based on the Euler product, where the spectral flow of energy levels provides a simple criterion for the validity of the Riemann Hypothesis and its generalizations, while also demonstrating how the absence of an Euler product leads to violations of the hypothesis.
This paper demonstrates that a vector-valued discrete Gaussian free field in two dimensions, conditioned to avoid a macroscopic ball, converges to a scaled equilibrium potential multiplied by a random unit vector, while also quantifying the exact capacity cost of this conditioning and establishing deterministic alignment across the domain.
This paper demonstrates that while the non-on-site symmetries of commuting-projector Hamiltonians like the 1+1d Ising model and 2+1d toric code cannot be made on-site using finite-dimensional ancillae due to fractionalized excitations, they can be disentangled into on-site symmetries by employing infinite-dimensional ancillae, provided the resulting ancilla Hamiltonians are unbounded from below.
This paper illustrates the critical role of the change-of-variables integration technique in graduate-level probability and statistics by demonstrating its application across seven examples, including the derivation of the Student's t-distribution's probability density function.
This paper presents a polynomial-time algorithm that samples from the Gibbs measure of the Sherrington-Kirkpatrick model with vanishing error for any inverse temperature by combining algorithmic stochastic localization with Jarzynski's equality, leveraging local regularity properties of the TAP free energy to extend previous results that were limited to .
This paper investigates the continuum limit of the para-Krawtchouk oscillator, demonstrating that its discrete Hamiltonian converges to a singular (isotonic) oscillator with a specific inverse-square potential, while its eigenvectors and algebraic structure transition to generalized Hermite functions and the dynamical algebra, respectively.
This paper demonstrates that the para-Racah Hamiltonian, a mirror-symmetric tridiagonal matrix with a quadratic bi-lattice spectrum, serves as an exactly solvable discretization of the Pöschl-Teller Hamiltonian, with the discrete model's recurrence relations, polynomial structures, and Racah algebra symmetry converging to their continuous trigonometric counterparts and Jacobi algebra as the number of sites increases.