1675 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 investigates unitary and open scattering quantum walks on arbitrary graphs parameterized by scattering matrices, demonstrating how they generalize existing models, form proper quantum channels, and exhibit spectral and dynamical properties linked to associated classical Markov chains.
This paper extends Washburn's capillary rise equation by incorporating a slip boundary condition, proving the global well-posedness of the resulting initial-value problem and characterizing the long-time dynamics, including monotonic or oscillatory convergence to equilibrium, for a wide range of slip parameters and initial fluid heights.
This paper investigates how to endow quantaloids with a compatible symmetric monoidal structure, demonstrating that dagger compact quantaloids share key properties with the category of relations and providing a framework for internalizing power sets and preorders to model discrete quantization and fuzzification.
This paper establishes a unifying framework for calculating mixed spectral moments of complex and symplectic non-Hermitian random matrices by deriving explicit formulas based on orthogonal polynomial norms, demonstrating their structural parallels to Hermitian limits, and performing large- asymptotic analyses for specific ensembles like the elliptic Ginibre and non-Hermitian Wishart matrices.
This paper proposes a method for constructing structure-preserving Jacobi Hamiltonian integrators by leveraging the correspondence between Jacobi and homogeneous Poisson manifolds to extend Poisson Hamiltonian Integrator techniques for modeling time-dependent, dissipative, and thermodynamic systems.
This paper establishes an arithmetic framework based on algebraic field theory and cyclotomic structures to rigorously determine exact, state-independent recurrence times in finite-dimensional Floquet systems, revealing that rational Hamiltonian parameters do not guarantee recurrence and providing efficient methods to identify or rule out such dynamics across both integrable and non-integrable models.
This paper presents a collection of infinite-dimensional nonholonomic and vakonomic systems, demonstrating how these dynamics arise as limits of holonomic systems with dissipation and exploring their applications ranging from sub-Riemannian geometry and fluid dynamics to the infinite-dimensional limit of a car with trailers.
This paper introduces the "shell formula," a unifying framework that provides explicit closed-form expressions and recursion relations for partition functions across diverse physical systems—including 5d super Yang-Mills instantons and various gauge origami configurations—by classifying their pole structures through arbitrary-dimensional Young diagrams.
This paper presents a fully covariant and gauge-invariant formulation of electromagnetic wave propagation in static black hole spacetimes that reduces both axial and polar sectors to a unified master equation, enabling the derivation of a closed-form, position- and frequency-dependent effective refractive index in Schwarzschild geometry to provide an intuitive optical framework for analyzing gravitational effects on wave dynamics.
This paper establishes a Hamiltonian framework for vortex clusters on a flat torus using the Schottky-Klein prime function, deriving a universal small-cluster expansion that reduces collective dynamics to a closed description governed by a single complex quadrupole moment, a prediction validated by numerical simulations.