3383 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 Löwdin symmetric orthogonalization (LSO) outperforms Gram-Schmidt orthogonalization in quantifying quantum resources like coherence and superposition by providing a symmetric, order-independent transformation and introducing non-negative Löwdin weights that ensure consistent, physically meaningful resource characterization.
This exploratory numerical study evaluates the potential for quantum advantage in solving network-based linear systems by analyzing 50 graph families across multiple quantum algorithms, identifying specific "good" families that offer exponential speedups over classical solvers, and proposing visual conjectures to predict these advantages while acknowledging practical hardware limitations.
This paper proposes a kinetic model based on Boltzmann-type equations to describe the coupled evolution of wealth and knowledge in national and global markets, demonstrating how individual interactions and international transfers lead to emergent Pareto tails in long-term distributions.
This paper presents a systematic framework for constructing (3+1)-dimensional fermionic topological quantum field theories that realize specified finite symmetry anomalies by translating supercohomology data into fusion 2-categories, ultimately proving that all supercohomology anomalies are realizable while beyond-supercohomology anomalies are not.
This paper establishes Davies-Gaffney-Grigoryan estimates for the heat kernel of the Hodge Laplacian on simplicial complexes, extends the associated semigroup to spaces under specific curvature and volume growth conditions, and proves the independence of the spectrum from for .
This paper extends multi-level Schauder estimates and a reconstruction theorem for germs of distributions from Euclidean space to smooth Riemannian manifolds by utilizing the exponential map and introducing a novel concept of -regularizing kernels, all without imposing additional geometric assumptions.
This paper establishes a variational principle for a large limit of the dimer model in any dimension , proving that random configurations concentrate on a unique limit shape determined by Euler-Lagrange equations and explicitly computable surface tension, thereby providing one of the first explicit solutions for limit shapes in statistical mechanics models of dimension three and higher.
This paper extends the characterization of Kirkwood-Dirac positivity to second countable locally compact abelian groups by linking the representation to Kohn-Nirenberg quantization, identifying positive pure states as Haar measures on closed subgroups, and establishing that the associated classical fragment is non-trivial if and only if the group possesses a compact identity component.
This paper extends the proof of the Hadamard property for the Unruh state of a free scalar field on Kerr-de Sitter spacetime to any subextreme black-hole rotation by generalizing geometric analysis of the trapped set, while also discussing its applications in numerical studies of inner horizon quantum effects and related universality results.
This paper derives Bethe ansatz equations for the spectra of the critical three-state Potts quantum chain with integrable twisted boundary conditions, demonstrating the completeness of the spectrum for small lattices and confirming that low-lying excitations exhibit fractional spins consistent with conformal field theory predictions.