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 derives the CH-KP equation, a mildly nonlinear model for quasi-unidirectional shallow water waves, from Euler equations using Hamiltonian reduction and long-wave asymptotics, while also analyzing its Hamiltonian structure and providing examples of weak peakon-type solutions.
This paper investigates the motion of a thin circular quantum vortex filament near an infinite planar surface in a parallel fluid flow, utilizing a novel quantization method to derive a complex energy spectrum and demonstrate the tensorial nature of the vortex's inverse effective mass, which can exhibit both positive and negative values in certain quantum states.
This paper establishes a rigorous framework for -deformed topological recursion by constructing all-order -WKB solutions for quantum curves, demonstrating their connection to -deformed algebras via shifted loop equations, and classifying the admissible parameters that ensure the semi-classical expansion is uniquely governed by this recursion.
This paper establishes Ward identities and Belavin-Polyakov-Zamolodchikov differential equations for Imaginary Liouville theory, providing a foundational step toward a rigorous conformal bootstrap program for non-rational conformal field theories with central charge less than one.
This paper rigorously establishes the Talbot effect for the periodic Benjamin--Ono equation with rough initial data by utilizing a smoothing gauge transform to derive explicit rational-time representations and prove continuity at irrational times under specific Diophantine conditions, thereby providing a structural explanation consistent with prior numerical observations.
This paper presents a rigorous construction and existence proof for a new family of exact general relativistic shock waves that match self-similar expanding spacetimes to static stellar models, demonstrating that such shock-wave spacetimes can exhibit accelerated expansion without a cosmological constant, thereby offering a potential mathematical alternative to dark energy.
Using Clifford algebra , this paper derives the 2D electron orbits of a hydrogen atom under circularly polarized light as a superposition of five Fourier terms, revealing that the resulting epicyclical motion approximates Keplerian orbits at specific frequency ratios while exhibiting discontinuities near resonance.
The paper argues that physical determinism is not independent of set-theoretic foundations, demonstrating that determinism verdicts for specific physical systems (such as Ising models and Kerr black holes) can vary between canonical extensions of ZFC like V=L and large cardinal assumptions, thereby proposing a field of "reverse physics" where the search for new axioms is continuous with the search for new physical laws.
This paper analyzes the spectral properties of the wave equation with distributional Dirac damping on compact intervals and star graphs, establishing that the spectrum is determined by the zeroes of an entire function, identifying critical damping values that alter spectral behavior, and deriving a definitive criterion for the Riesz basis property of root vectors.
This paper demonstrates that the genus of the algebraic spectral curve for a two-channel operator pencil with a power-law response is determined solely by the denominator of the rational exponent , yielding a genus of for , with specific applications to conformal response models and the Sachdev--Ye--Kitaev model.