1605 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 reformulates the Tolman-Oppenheimer-Volkoff equations for static, spherically symmetric perfect-fluid stars within the semi-tetrad formalism as a covariant first-order dynamical system, enabling a geometric analysis of stellar structure through autonomous flows in phase space for both linear and general equations of state.
This paper demonstrates that Abelian -duality on ALE spaces transforms the Maxwell partition function from a scalar into a vector-valued boundary state composed of theta-function blocks, which exhibit modular covariance and encode higher-form symmetry data, thereby establishing ALE spaces as chiral building blocks that glue to reproduce standard closed-manifold partition functions.
This paper introduces MARUT, a scalable, GPU-accelerated high-order CFD framework featuring adaptive mesh refinement and finite-rate chemistry capabilities, designed to deliver high-fidelity simulations of compressible and reacting flows across subsonic to hypersonic regimes on exascale supercomputing architectures.
This paper establishes a generalized Minkowski theorem for constant-curvature Lorentzian spaces by proving that four non-trivial holonomies uniquely reconstruct a strictly convex tetrahedron in de Sitter or anti-de Sitter space under specific closure and convexity conditions, while also characterizing the resulting polar-dual projective tetrahedra and recovering classical Euclidean and hyperbolic reconstruction results in the spacelike sector.
This paper introduces a representation-dependent diagnostic called the "coherence matrix" to test the stability of finite-separation flow geometry across observational resolutions, demonstrating through synthetic fields, Lorenz dynamics, and renormalization-group flows that this metric reveals structural inconsistencies in representations, models, and truncations that standard local or spectral diagnostics may miss.
This paper presents an exact analytical solution for the non-Hermitian XY spin chain with complex anisotropy and open boundaries, demonstrating that its quasi-energy spectrum retains a free-fermion structure while explicitly constructing biorthogonal and generalized eigenvectors at exceptional points to reveal their role as branch points that permute eigenstates upon encirclement.
This paper establishes a spectral cut-off construction using finite-dimensional time-sliced oscillatory integrals to prove the convergence of approximate propagators to the strong solution of non-autonomous Hamiltonian evolution equations, while also connecting this framework to Floquet–Magnus expansions and renormalized traces.
This paper introduces a symmetric tridiagonal matrix-valued process with stochastic resetting, demonstrating that simultaneous resetting yields an analytically solvable stationary eigenvalue distribution identical to resetting Dyson Brownian motion, while independent resetting produces a distinct ensemble that is studied numerically and applied to compute the annealed partition function of a disordered quantum system.
This paper investigates the recurrence of x-periodic anomalous waves in multidimensional nonlinear Schrödinger equations within a quasi-one-dimensional regime, demonstrating that while the initial instability stage is universal across models, subsequent dynamics exhibit model-specific differences characterized by increasingly complex fission and fusion processes, which are analytically described using finite gap perturbation theory.
This paper introduces a fully extrinsic, parametrization-free, and component-free tensor calculus framework for embedded submanifolds of arbitrary codimension, featuring an algorithmic recursive notation that facilitates both theoretical analysis and practical applications in fluid dynamics, continuum mechanics, and evolving geometry.