3190 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 note explains key elements of the proof by Y. Deng, Z. Hani, and X. Ma that extends Lanford's derivation of the Boltzmann equation from hard-sphere dynamics from a short-time interval to arbitrary large times, provided the Boltzmann equation admits a regular solution.
This paper establishes a unifying Koopman operator framework that characterizes the computational properties of dynamical systems by linking halting, reachability, and decidability to spectral features such as eigenfunctions and invariant subspaces, thereby bridging symbolic and analog computation through operator-theoretic signatures.
This paper strengthens the classification of one-dimensional Fermionic cellular automata by removing the need for ancillary systems in defining equivalence classes, provides a complete characterization of nearest-neighbor automata, and identifies a distinct class of Fermionic automata that cannot be constructed using single-mode and controlled-phase gates combined with shifts, unlike their qubit counterparts.
This paper constructs a strongly rational, completely unitary chiral algebra of central charge eight whose representation category is equivalent to the Drinfeld center of the Haagerup fusion category, thereby providing a concrete realization of a Haagerup conformal field theory.
This paper demonstrates that the work distribution for sudden quantum quenches in translation-invariant quadratic fermionic chains can be mapped to the statistics of traces of Haar unitary matrices, yielding a Gaussian distribution via multivariate central limit theorems while also characterizing the specific conditions—such as long-range interactions or Fisher-Hartwig singularities—that lead to non-Gaussian deviations.
This paper establishes a necessary and sufficient condition for the renormalizability of quantum cellular automata by defining a coarse-graining procedure that groups cells into tiles, and applies this framework to exhaustively solve and identify the fixed points of the renormalization flow for qubit-based automata on a one-dimensional line.
This paper demonstrates that for radially symmetric Schrödinger operators on with a potential composed of two distinct spatial scales, the total count of positive eigenvalues is exactly the sum of the positive eigenvalue counts associated with each scale's individual potential, a result established through a novel framework combining dynamical systems techniques with a separation of scales argument.
This paper establishes supercritical sharpness for the Ising double random current model in dimensions by proving local uniqueness of the macroscopic cluster via a simplified sprinkling argument, thereby offering a more accessible proof of exponential decay of truncated correlations and exponential mixing for the FK-Ising measure.
This paper proves a conjectured factorized formula for the determinant of an evaluation matrix associated with a degeneracy graph by establishing a block-triangular structure via graph analogues of Newton polynomials, thereby revealing that the determinant's exponents correspond to overlap volumes of higher-dimensional Young diagrams and enabling the explicit recursive inversion of the matrix.
This paper extends the Bogomolny–Zinn-Justin cancellation mechanism to multi-well quantum systems by deriving multi-instanton contributions from Euclidean path integrals, demonstrating how Picard–Lefschetz relations between integration contours reproduce exact-WKB Stokes jumps, and identifying ambiguities in event sequence mappings at higher nonperturbative orders.