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 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.
This paper extends the integrability-preserving renormalization-group (RG) protocol to non-Hermitian quantum systems with time-dependent interactions, demonstrating that the set of such integrable models is broader than the standard RG trajectories because it also includes specific time-dependent forms for RG-invariant couplings.
This paper revisits the Moore-Read construction of Laughlin states on compact Riemann surfaces by deriving their conformal blocks from Chern-Simons theory, computing explicit monodromies for quasi-hole transport and flux insertion, and demonstrating how these results recover classical Hall conductance values while connecting to modern algebro-geometric approaches.
This paper establishes that a conservation law of integer phase charge in squeezed-light reservoirs fundamentally limits their computational expressivity and readout cost, demonstrating that detector constraints rather than optical nonlinearity dictate which functionals can be efficiently computed.
This paper proves that Brownian motion conditioned on a time-average constraint for a confining potential converges locally to a ground-state diffusion, providing sharp asymptotics for the conditioning probability and resolving a conjecture by extending previous one-dimensional results to arbitrary finite dimensions and various reversible Markov processes.
This paper constructs nonunitary 2d gauged linear sigma models with supergauge groups to establish super-Grassmannian generalizations of key mathematical correspondences, including Calabi-Yau/Landau-Ginzburg dualities, birational equivalences via flop transitions, and homological projective dualities via conifold transitions.