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 investigates Burgers-type fluid dynamics under gravitational fields by deriving perturbative expressions for the catastrophe time in both Newtonian and Schwarzschild spacetimes, demonstrating that the validity of the expansion is governed by a specific dimensionless parameter rather than local gravitational acceleration alone.
This paper derives conservation laws for time-dependent damped nonlinear multidimensional wave equations using Noether's theorem, identifying that while arbitrary damping and nonlinearity yield Euclidean symmetries producing linear and angular momentum conservation, specific forms of these terms enlarge the symmetry algebra to a subalgebra of the conformal group, resulting in additional conserved quantities.
This paper demonstrates through a counting argument that translation symmetry enforces long-range entanglement in mixed states, specifically showing that the strong-to-weak spontaneous symmetry breaking fixed point cannot be represented as a mixture of short-range entangled states despite the existence of symmetric short-range entangled eigenstates.
This paper investigates the impact of boundary vorticity distribution on enstrophy dynamics for flows around streamlined bodies by deriving a new energy identity and establishing enstrophy dissipativity for the Stokes system, alongside a novel enstrophy dynamics equation for the Navier-Stokes system.
This paper establishes a rigorous mathematical foundation for the Martin-Siggia-Rose path integral formalism by deriving an exotic B-series representation of the Feller semigroup for one-dimensional Itô diffusions and demonstrating its exact equivalence to the perturbative path integral construction.
This paper presents a method for constructing polynomial superintegrable magnetic geodesic flows on reductive homogeneous spaces by generating two commuting families of first integrals from the Lie algebra and an invariant affine slice, thereby establishing a reduced Poisson algebra that yields superintegrable systems with explicit action-angle coordinates, as demonstrated in specific SU(3) examples.
This paper derives a heterogeneous Cattaneo-Vernotte equation from stochastic interpretations of diffusion with position-dependent coefficients, providing exact solutions for probability density and mean squared displacement that reveal ergodicity breaking in the system.
This paper investigates the unitary invariance of Connes spectral distances in finite-dimensional spectral triples, deriving elementary properties of optimal elements and demonstrating that specific constructions can yield distances equivalent to quantum trace distances.
This paper establishes the -contact Hamilton–De Donder–Weyl formalism as a comprehensive geometric framework for modeling dissipative field equations, providing essential analytical tools and explicit Hamiltonian descriptions for a wide range of nonlinear nonconservative partial differential equations.
This paper proposes a variational framework for modeling accretive surface growth in elastic structures by determining configurations through constrained minimization of structural mean compliance, leading to a time-continuous constrained gradient flow that accounts for growth-induced residual stresses and potential nonuniqueness.