1666 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 trace-Dobrushin theory for quantum channel products to establish conditions for asymptotic replacement and memory loss in both deterministic and stationary random settings, subsequently applying these results to derive infinite-volume limits, boundary stability, and correlation bounds for inhomogeneous matrix product states.
This paper establishes a Generalized Fourier Transform on Riemannian manifolds by resolving spectral degeneracies through symmetry-adapted maximal Abelian commuting sets, thereby constructing a rigorous framework for momentum-space analysis that unifies geometric constraints with unitary mode decompositions.
This paper proves that for the Anderson model on the Bethe lattice in the strong-disorder regime with compactly supported, locally analytic single-site distributions, the root-averaged density of states is absolutely continuous and admits a finite-order, real-analytic expansion where all odd coefficients vanish and higher-order terms are determined by short closed walks on the tree.
This paper establishes a large deviations principle for the supremum of solutions to the Korteweg-de Vries equation with random initial data over polynomial timescales, demonstrating that unusually large wave amplitudes arise primarily from the quasi-synchronization of phases rather than resonant energy exchange, due to the stability of the equation's integrable dynamics.
This paper introduces Unbalanced Schrödinger Bridge (USB), a simulation-free framework that overcomes the limitations of existing continuous Optimal Transport methods by rigorously modeling discrete, jump-like birth-death dynamics at single-cell resolution to reconstruct cellular lineage trajectories from destructive snapshots.
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.