2619 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 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.
This paper demonstrates that introducing an arbitrarily small friction term into the multidimensional axisymmetric Euler-Poisson equations for cold plasma ensures global smoothness and asymptotic stabilization to zero, thereby preventing the blow-up phenomena observed in the frictionless case.
This paper presents a generic formulation for the quantum geometric dipole (QGD) of collective excitations in many-body electron systems that relies on the density matrix rather than specific single-particle wavefunctions, demonstrating its validity and intrinsic nature across both integer and fractional quantum Hall states.
This paper proposes a proof of the Riemann Hypothesis by constructing a one-dimensional quasicrystal from the logarithms of prime numbers, demonstrating that the Fourier self-duality of its scattering amplitude forces the real parts of all non-trivial Riemann zeta zeros to equal 1/2.
This paper introduces a novel exclusion process with a local kinetic constraint that exhibits a phase transition from a homogeneous state to a clustered, translation-invariance-breaking state, characterized by glassy coarsening dynamics and a counterintuitive "faster-is-slower" effect where increased flow asymmetry reduces the stationary current.