3217 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 analytically characterizes the adjacency matrix spectra of random graphs with discrete scale invariance and infinite-mean node fitness, revealing that their leading eigenvalues form a logarithmic spiral with alternating signs and that their eigenvectors exhibit log-periodicity, distinguishing them from typical finite-rank random graph models.
This paper proposes a fast, stable, and direct analytic method using one-dimensional shallow water equations to reconstruct underwater channel topography from surface wave measurements at a single instant, demonstrating high accuracy and Lipschitz stability under specific discharge conditions.
This paper investigates the implications of modified Painlevé-Gullstrand coordinates for Kiselev black holes surrounded by quintessence by constructing a static line element with a deformation parameter, analyzing radiation and dust effects via the barotropic index, and deriving closed-form expressions for Hawking temperature and entropy.
This paper provides a simple and elementary proof, utilizing high-temperature expansion, random-cluster, and random current representations, that the truncated two-point function of the near-critical planar Ising model on with external field decays exponentially.
This paper derives exact solutions to the one-dimensional Schrödinger equation for compactly supported parabolic and hyperbolic secant potential barriers (including their combinations), providing explicit expressions for transmission and reflection coefficients as well as specific dwell times.
This paper establishes the existence of minimizers and the sharp stability of the ball for a liquid drop model perturbed by a Yukawa potential, demonstrating that the competition between surface tension and repulsion is governed by two independent parameters (screening rate and volume) and overcoming technical challenges posed by the kernel's lack of homogeneity.
This paper establishes an optimal Poincaré inequality and determines the exact spectral gap for real-valued symmetric observables of the complex Ginibre log-gas by combining a Vandermonde transform, holomorphic projection, and a complex Gaussian -spectral-gap estimate to overcome the challenges posed by the unbounded Hessian of the system's energy.
This paper presents provably efficient classical algorithms for simulating the real-time dynamics of weakly interacting fermionic systems on geometrically local lattices by leveraging a new Heisenberg-picture operator-growth analysis to rigorously control sampling variance in regimes where interactions are sufficiently weak or localized.
The paper proposes that partial quantum entanglement creates a network of particles with long-range connections sufficient to establish a small-world structure throughout the universe on all scales except those of stars and planets.
This paper establishes the first global strong well-posedness and exponential asymptotic stability for the spatially homogeneous four-wave kinetic equation associated with the cubic nonlinear Schrödinger equation, proving that small perturbations of Rayleigh-Jeans equilibria relax exponentially due to a spectral gap in the linearized operator and controlled nonlinear interactions.