2548 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 demonstrates that in the incompressible two-dimensional case, both Legendre-Hadamard ellipticity (rank-one convexity) and polyconvexity imply Hill's inequality, thereby clarifying the intimate connection between these previously considered independent constitutive conditions.
This paper introduces a geometric-analytic framework for equilibrium statistical mechanics on infinite-dimensional Hamiltonian systems by utilizing normalized means to define entropy and free-energy functionals, thereby establishing the existence and uniqueness of exponential-family equilibrium states and their thermodynamic properties without relying on -additive invariant measures.
This paper derives exact evolution formulas and explicit density profiles for the symmetric Dyson exclusion process by leveraging its representation as a ground-state transform of the spin-1/2 XX chain, revealing a governing polynomial algebra with Catalan number coefficients and confirming previously conjectured hydrodynamic results.
This paper establishes a classification framework for structured Keyfitz-Kranzer systems of conservation laws by analyzing how specific structural conditions on the flux function dictate the finite-time blow-up of solution amplitudes and determine whether Riemann problem solutions are classical or involve delta-shocks and vacuum states.
This paper investigates the inverse spectral problem for a Sturm-Liouville operator on a star-like metric graph with non-local boundary conditions and a one-point interaction at the vertex, demonstrating that the network's topology can be recovered under specific necessary conditions by analyzing non-local characteristic functions and eigenvalues.
This paper introduces a strength-degradation phase-field model for antiplane fracture that unifies limit analysis, plasticity, and various fracture regimes by decoupling strength, stiffness, and toughness, thereby allowing crack nucleation and propagation to be governed by an arbitrary convex strength surface and an elasto-cohesive length scale rather than being constrained by elastic energy.
This paper demonstrates that applying a stress-free boundary condition at the bottom of the Ekman layer yields an unphysical current profile where velocity increases with depth, while showing that a no-slip condition at sufficient depth still effectively preserves the orthogonality between Ekman transport and wind stress.
This paper establishes the large deviation principle for the maximum of the generalized TAP free energy in the Ising mixed -spin model by proving that supersymmetric critical points form a spherical code, thereby identifying the supersymmetric formula with the large-deviation exponent for TAP maxima and providing a constructive path toward the Parisi formula under specific stability conditions.
This paper proposes an inflationary mechanism driven by flux stationarity near Calabi-Yau Hodge boundaries, which stabilizes moduli without extra flux costs and directly links internal geometric properties to observable primordial tensor perturbations that align with current CMB limits and future LiteBIRD and CMB-S4 targets.
This paper demonstrates that a nonlinear velocity theory for extreme type-II superconductors contains an exactly solvable one-dimensional sector yielding universal nonlinear Meissner states, soliton-like vortex sheets interpreted as coarse-grained Abrikosov vortex rows, and periodic laminar structures representing rectangular vortex lattices.