2548 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 proposes a minimum-energy collective steering framework for inertial swarms subject to stochastic disturbances and governed by mean-field interaction models, utilizing Schrödinger bridge theory to derive optimal state-feedback controls that steer the system between prescribed endpoint distributions by dynamically exploiting or counteracting natural interaction forces.
This paper presents a stable, fully 3D Summation-by-Parts scheme for linear wave equations on hyperboloidal foliations of Minkowski spacetime. It effectively addresses the coordinate singularities associated with curvilinear coordinates and infinity through compactification. Additionally, it generalizes the definition of Kreiss-Oliger dissipation to curvilinear coordinates on general spatial manifolds, demonstrating promising results for future applications to nonlinear systems, such as the Einstein Field Equations.
This paper resolves a long-standing open problem by proving the missing lower bound for the leading low-temperature free-energy asymptotics of the two-dimensional quantum Heisenberg ferromagnet, thereby confirming Takahashi's prediction and completing the rigorous derivation of the limit.
This paper establishes that the affine varieties arising as monodromy surfaces for Painlevé equations VI, IV, II, and I are embedded affine del Pezzo surfaces, and demonstrates that their monodromy groups correspond to the finite parts of the associated affine Weyl symmetry groups through analytic, Galois-theoretic, and combinatorial realizations.
This paper establishes lower bounds on the pointwise spatial decay of the ground state for both the full Pauli-Fierz model and its dipole approximation, utilizing a probabilistic Feynman-Kac approach for the former due to path-dependent stochastic complications and the Agmon distance method for the latter where the integrand becomes deterministic.
This paper investigates the time-integrated current statistics in an infinite one-dimensional gas of independent active Ornstein-Uhlenbeck particles, revealing distinct diffusive, super-diffusive, and sub-diffusive regimes governed by a single scaled cumulant generating function, a persistent memory of initial conditions, and temporal correlations, all validated by rare-event importance sampling capable of resolving probabilities as low as .
This paper demonstrates that the moduli space of quasimaps from to a Nakajima quiver variety, with a fixed value at infinity, can be globally realized as the critical locus of an explicit function.
This paper demonstrates that the superadditivity of classical communication over quantum channels, originally proven using Haar random unitaries, can be established using random permutations and subsequently derandomized via deterministic algorithms, although the resulting explicit counterexamples remain computationally infeasible due to their enormous dimension.
This paper unifies the fundamental components of plasticity theory—including yielding, flow, and hardening—into a single scalar functional framework based on directional stationarity over one-sided admissible paths, thereby deriving elastic inequalities, loading-unloading conditions, and both associated and non-associated flow rules while accommodating various hardening mechanisms and rate-dependent evolution.
This paper proves Fyodorov's 2006 conjecture by demonstrating that for Gaussian random matrices from the GOE and GUE ensembles, the normalized zero counting measure of the permanental characteristic polynomial converges almost surely to a Wigner semicircle law rotated by onto the imaginary axis.