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 develops a classical model-theoretic framework using partial Boolean algebras to demonstrate that quantum-like uncertainty and the Kochen-Specker theorem can arise from the structural organization of propositions and models without abandoning classical propositional logic.
This paper presents a second-order unfitted ghost finite element method for solving elliptic interface problems on fixed Cartesian grids, which is validated on benchmarks and successfully applied to simulate the electrostatic behavior and transfer characteristics of graphene field-effect transistors within a self-consistent drift-diffusion-Poisson framework.
This paper establishes explicit asymptotic formulas for the eigenvalues of the one-particle density matrix and kinetic energy density operators associated with -particle atomic eigenfunctions, demonstrating that their decay rates are determined by particle coalescence singularities and are significantly faster when the eigenfunction is totally antisymmetric.
This paper presents a design space study of density matrix parameterizations for diffusion-based quantum state tomography, introducing a geometric framework based on the Jacobian Gram matrix to reveal that isometric conditioning and physical constraint satisfaction are orthogonal criteria where no single parameterization optimizes both, and demonstrating that while better-conditioned parameterizations improve convergence and fidelity without classifier-free guidance, the inclusion of such guidance can reverse performance rankings due to amplified boundary effects.
This paper introduces a generalized preferential attachment model for hypergraphs that analytically predicts a power-law degree distribution dependent on the ratio of new nodes to hyperedge size, and demonstrates through empirical analysis that preferential attachment acts as a mechanism enforcing simpliciality in real-world networks.
This paper introduces a topological superselection profile framework based on Koszul-complex stabilizer models to characterize translation-symmetry-enriched topological phases in CSS codes, demonstrating that while single-layer cohomology determines rigidity for regular models, the inter-layer gluing data in nonsplit extensions is essential for distinguishing distinct phases that share identical excitation spectra.
This paper presents a novel, simple range characterization for the spherical mean transform in odd dimensions based on symmetry relations of spherical harmonic coefficients and a new cross product identity for Bessel functions, which is subsequently used to disprove unique continuation results for this transform.
This paper derives joint splitting probabilities for two-dimensional drift-diffusive processes to define conditional splitting probabilities, which are then used to propose a scheme for inferring hidden internal states from observable exit events.
This paper introduces a nonlinear Lorentz-invariant kinetic diffusion equation that conserves particle number, energy, and momentum, converges to the Maxwellian distribution in the Newtonian limit rather than the Jüttner distribution, and is compatible with Einstein's equations on general Lorentzian manifolds.
This paper establishes a robust bulk-boundary correspondence for two-dimensional non-Hermitian systems by utilizing Toeplitz operators and singular values—rather than unstable eigenvalues—to precisely characterize the stability, localization, and scaling of edge and corner modes without requiring crystalline symmetries.