🔢 Category

math-ph

3210 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.

🔢 mathematics

Aldous' spectral gap phenomena in stochastic exchange models

This paper establishes that for a broad class of conservative continuous-spin exchange models, the spectral gap is always determined by a polynomial of degree at most two (corresponding to one- or two-particle observables), thereby resolving a conjecture by Alon and Puder and characterizing how the dominance of one- versus two-particle modes depends on the underlying geometry, while also showing that boundary-driven variants of these systems always exhibit a one-particle spectral gap.

Pietro Caputo, Matteo Quattropani, Federico Sau2026-09-10
🔢 mathematics

Open Inextensible Filaments in Planar Stokes Flow: Well-Posedness, Endpoint Asymptotics, and Straightening

This paper establishes the local well-posedness of the third-order nonlocal curvature equation governing open inextensible filaments in planar Stokes flow for nearly critical initial data, while demonstrating that finite-time singularities necessitate a loss of the arc-chord condition and that global solutions either exponentially straighten or exhibit vanishing arc-chord constants.

Han Zhou2026-09-10
🔢 mathematics

Fluctuations of additive martingale limits of branching Brownian motion

This paper strengthens the known convergence of the additive martingale limit to the derivative martingale limit in branching Brownian motion from convergence in probability to almost sure convergence, while further characterizing the fluctuations around this limit as a spectrally negative 1-stable distribution and extending these results to complex and multi-dimensional settings.

Xinxin Chen, Michel Pain2026-09-10
⚛️ general relativity

On Twisted Spacetimes: a new class of Galilean cosmological models

This paper introduces Galilean Twisted spacetimes within generalized Newton-Cartan theory as duals to relativistic twisted spacetimes, demonstrating that the local and global structures of spacetimes admitting timelike torqued vector fields correspond to these models while also analyzing the completeness of free-falling and general observers.

Daniel de la Fuente, Rafael M. Rubio, Jose Torrente-Teruel2026-09-09
🔢 mathematics

Nonequilibrium steady state in Lindblad dynamics for infinite quantum spin systems

This paper establishes a C∗C^*-algebraic framework for nonequilibrium steady states in infinite quantum spin systems and provides a sufficient condition, involving a Liouvillian condition number and spectral gaps, to ensure that the steady state of the infinite system coincides with the thermodynamic limit of finite-system steady states, thereby addressing cases where time and thermodynamic limits fail to commute despite uniform spectral gaps.

Kenji Shimomura, Nagisa Hara, Seiichiro Kusuoka2026-09-09
🔢 mathematics

Controlled atomic limit and analytic density of states in a strongly attractive random Kronig-Penney model

This paper establishes a controlled atomic limit and proves the real-analyticity of the density of states for a one-dimensional random Kronig-Penney model with strong attractive interactions by reducing the continuum problem to a lattice operator and demonstrating that the scaled density of states converges exponentially fast to that of isolated bound states.

Masahiro Kaminaga2026-09-09