3307 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.
Using Clifford algebra , this paper derives the 2D electron orbits of a hydrogen atom under circularly polarized light as a superposition of five Fourier terms, revealing that the resulting epicyclical motion approximates Keplerian orbits at specific frequency ratios while exhibiting discontinuities near resonance.
The paper argues that physical determinism is not independent of set-theoretic foundations, demonstrating that determinism verdicts for specific physical systems (such as Ising models and Kerr black holes) can vary between canonical extensions of ZFC like V=L and large cardinal assumptions, thereby proposing a field of "reverse physics" where the search for new axioms is continuous with the search for new physical laws.
This paper analyzes the spectral properties of the wave equation with distributional Dirac damping on compact intervals and star graphs, establishing that the spectrum is determined by the zeroes of an entire function, identifying critical damping values that alter spectral behavior, and deriving a definitive criterion for the Riesz basis property of root vectors.
This paper demonstrates that the genus of the algebraic spectral curve for a two-channel operator pencil with a power-law response is determined solely by the denominator of the rational exponent , yielding a genus of for , with specific applications to conformal response models and the Sachdev--Ye--Kitaev model.
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.