1668 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 reflection symmetry and Atiyah-Patodi-Singer boundary conditions for twisted Dirac operators on a warped cylinder, establishing that reflection compatibility requires a specific holonomy quantization and demonstrating how spectral flow decomposes into equivariant or mod-two invariants depending on whether the holonomy is fixed or varying.
This paper extends the optimal control formulation of incompressible ideal flows by introducing a barrier-type potential to enforce obstacle avoidance, which results in modified Euler equations where the barrier acts as a localized pressure shift and induces flow deformation near obstacles.
This paper investigates quantum transport on finite-generation Bethe lattices with non-Hermitian sources and a drain, revealing that the current reaches a maximum at a zero mode—often an exceptional point in -symmetric systems—where only a limited number of eigenstates effectively penetrate from the periphery to the center, while the remaining states remain localized.
This paper establishes a synthetic framework for null hypersurfaces in non-smooth spacetimes by defining a synthetic null energy condition via optimal transport, which generalizes classical results to singular settings and enables the proof of Hawking's area theorem and Penrose's singularity theorem in continuous and topological causal spaces.
This paper establishes a local exponential stabilization framework for McKean-Vlasov PDEs on the torus by employing a ground-state transform to enable spectral analysis and Riccati-based feedback control, thereby accelerating convergence to stationary distributions and stabilizing unstable equilibria as validated by numerical experiments.
This paper applies stochastic calculus and Girsanov transformations to the Fermi-Hubbard model to derive a factorization-independent representation of thermodynamic correlation functions, which analytically proves the antiferromagnetic nature of spin-spin correlations at half-filling and enables the approximation of ground state energies via ordinary differential equations.
This paper analytically derives the full statistical properties of the maximally dispersed subset of random points in using mean-field theory and the replica method, revealing that for large populations and rotationally symmetric distributions, the optimal subset comprises all points lying outside a self-consistently determined -dimensional ball.
This paper analyzes planar -body Hamiltonian systems with -invariant interactions to demonstrate that while superintegrability ensures periodicity through frequency commensurability, true collision-free choreographies require a stricter sectorwise phase-matching condition that restricts such solutions to single irreducible sectors or exact degeneracies, as explicitly illustrated in cases .
The paper establishes the existence of an effective light-cone for entanglement propagation in bipartite systems with localized couplings, thereby defining a fundamental lower bound on the time required to transport or maintain entanglement across distant locations in an ideal quantum network.
This paper establishes a quantum group-theoretical framework for long-range deformations of homogeneous Yang-Baxter integrable spin chains by demonstrating that these deformations arise from a twist of the underlying algebra, resulting in a non-associative structure with a Drinfeld associator that encodes interaction terms while preserving perturbative integrability through a large associative substructure.