2656 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 presents a unified framework for constructing continuous and discrete -invariant integrable systems by generalizing the Schwarzian derivative and cross-ratio through the factorization of third-order linear spectral problems, thereby establishing dualities, exact discretizations, and a generating Lagrangian structure for the Boussinesq hierarchy.
This paper demonstrates that on a codimension-one manifold of fine-tuned initial data, the internal mode of a soliton in the 1D quadratic Klein-Gordon equation undergoes slow, irreversible decay into dispersive radiation due to radiation damping, a process accurately described by a cubic resonant approximation with a damping rate governed by a Fermi golden rule-type coefficient.
This paper proves that isotropic spin and field models on the one-dimensional integer lattice satisfy the generalized Lee-Yang property for all even dimensions , extending a result previously known only for two-dimensional isotropic models.
This paper constructs and analyzes the stability of single-frequency asymptotic solutions for damped driven Maxwell-Bloch equations under quasiperiodic pumping, utilizing the Bloch-Feynman gyroscopic representation and Bogolyubov-type averaging theory.
This paper establishes a unified categorical framework for defining decorated Betti moduli spaces on surfaces with boundary marked points, thereby systematically connecting various existing approaches to studying representations of fundamental groupoids with irregular singularities.
This paper formulates a Markov decision process for the low-temperature metastable Ising model under Kawasaki dynamics to determine optimal strategies for guiding a particle cluster to a fully occupied state, revealing that efficiency-based rewards favor growth at cluster boundaries while energy-based rewards favor growth at corners.
This paper establishes the well-posedness of the -problem associated with the AKNS spectral system by developing a decomposition technique to prove the existence and uniqueness of solutions under small norm conditions, while extending the Dbar dressing method to construct potentials and demonstrating the Lipschitz continuity of the map from Dbar data to the potential.
This paper presents a stable and efficient numerical method for solving acoustic multibody scattering problems in two and three dimensions by combining local Method of Fundamental Solutions (MFS) approximations with a global iterative solver, achieving high accuracy and scalability without the implementation complexity of traditional boundary integral discretization techniques.
This paper proves that recognizing the phase of matter for unknown quantum states is quantum computationally hard, requiring exponential time in the correlation range for a wide class of phases including symmetry-breaking and symmetry-protected topological phases, by demonstrating the existence of symmetric pseudorandom unitaries under standard cryptographic conjectures.
This paper proves that the spectral radius of the ratio of two independent Girko matrices, when scaled by the square root of the dimension, converges to a universal heavy-tailed distribution as the dimension tends to infinity, a result established through Girko Hermitization and local law estimates that reveals the model's remarkable mathematical accessibility compared to single Girko matrices.