1694 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 introduces a Gagliardo-type framework for fractional Sobolev spaces on arbitrary time scales using the Lebesgue -measure and off-diagonal interaction energies, establishing their Banach and Hilbert space properties, proving Poincaré-type inequalities that reflect the underlying geometry, and unifying continuous, discrete, and hybrid settings.
This paper investigates the topological content of the Zak phase in one-dimensional topological insulators across all Altland-Zirnbauer-Cartan symmetry classes, demonstrating how to construct a -valued invariant from the Zak phase while revealing that quaternionic structures imposed by specific anti-unitary symmetries force this invariant to vanish.
This paper establishes that Csanyi's and Arias' energy functional is bounded between the Müller and Hartree-Fock functionals, a result used to derive an asymptotic expansion of the ground state energy that matches the quantum energy up to the third order.
This paper demonstrates that while a ghost Hamiltonian and its classically equivalent alternative formulation yield identical classical trajectories, they produce distinct Bohmian quantum dynamics, thereby revealing a concrete quantum ambiguity where classical equivalence fails to extend to the quantum regime in higher-derivative systems.
This paper analyzes a discrete-time binary branching random walk with a repulsion penalty for close particles, demonstrating that the optimal configurations at time exhibit a spatial spread of order and incur a total cost of order .
This paper extends the universality of the point process to a general class of -additions of Gaussian and Laguerre ensembles by introducing a Type-A Bessel function and utilizing Dunkl operators to derive a universal limiting expression for the Laplace transform of in terms of conditional Brownian bridges.
This paper computes the -equivariant topological Euler characteristic of the Kontsevich moduli space by deriving a closed formula for the non-rational-tail subspace via torus localization and expressing the full result through plethysm with a genus-zero contribution.
This paper proves that solutions to the kinetic transport equation derived from the two-dimensional periodic Lorentz Gas converge to an equilibrium state in the norm under periodic boundary conditions, utilizing Fourier coefficient analysis to establish convergence rates for specific cases.
This paper introduces a general method based on the transverse intersection of submanifolds in phase space to prove the non-degeneracy of the Hessian in spinfoam vertex amplitudes with a cosmological constant, thereby validating the stationary phase approximation for non-degenerate geometric 4-simplices in de Sitter or anti-de Sitter space and confirming the model's connection to semiclassical gravity without dominant exceptional contributions.
This paper presents an exact analytical solution for time-evolving resonant states in an open double quantum-dot system with spin and Coulomb interactions, deriving a non-Hermitian effective Hamiltonian that identifies four types of two-body resonant states and enables the precise calculation of survival and transition probabilities for localized electrons.