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 constructs a tau function for the -difference sixth Painlevé equation as a Fredholm determinant via a Riemann-Hilbert problem, establishing its analytic properties, expressing the equation's transcendents in terms of shifted tau functions to characterize exceptional initial values, and deriving its small-time asymptotic expansion.
This paper investigates the geometric structure of spectra for absolute separable and absolute PPT quantum states, establishing that while the latter forms a spectrahedron with fully characterized faces, the former is generally a semialgebraic set, and providing rigorous bounds on their purity, entropy, and relative spectral volume.
This paper introduces a fractional Fibonacci number system to derive a localization criterion for the many-body non-interacting Aubry-André model, where particle density is expressed in this system for finite sizes and in base- for the thermodynamic limit.
This paper establishes that for a class of partition functions on the Boolean cube with 1-Lipschitz, bounded-dependency functions, the zero-free region is preserved under a linear increase in multi-spin interaction energies provided the external field increases only logarithmically, thereby keeping the system away from phase transitions.
This paper proposes a fast numerical implementation, based on the work of Siewert and Maiorino (1980), to handle the Dirac singularity caused by collimated sunlight in atmospheric radiation models used for calculating Earth's air temperature.
This paper proposes and validates a reduced-order modeling approach for electromagnetic inverse problems in layered media, demonstrating that a ROM-based objective function yields superior impedance profile reconstructions in clean and certain perturbed scenarios compared to classical data misfit methods.
This paper combines theoretical predictions, experimental validation using magnetized colloids, and numerical simulations to demonstrate that overdamped particle suspensions under repulsive power-law potentials exhibit self-similar spreading, while below a critical power threshold, particles accumulate at the perimeter to retain a long-lived memory of their initial distribution.
This paper proposes a reformulated swap approach to the minimal string/matrix model duality that resolves previous conceptual difficulties by eliminating the need for resonance transformations and enabling a new conjecture for computing non-tachyon amplitudes.
This paper employs matched asymptotic expansions to derive three-term asymptotic formulas for the mean first-reaction time, splitting probabilities, and spectral properties of mixed Steklov-Neumann problems in a 3D spherical domain with small, partially reactive surface patches, accounting for arbitrary reactivities and spatial configurations.
This paper establishes the existence of thermodynamic limits and proves that two-point correlations in stochastically generated matrix product states decay exponentially or polynomially depending on the mixing properties of the underlying strictly stationary tensor distribution, thereby unifying and extending recent results on random MPS ensembles through a transfer-operator framework.