3358 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 presents an exact solution for the convex roof of the square root of the three-tangle for rank-two density matrices and all states within the Bloch sphere, identifying new optimal tetrahedra and triangular decompositions governed by a "zero-state locking" property that extends to all SL-invariant GHZ and W states and is applicable to arbitrary qubit numbers.
This paper demonstrates that 't Hooft anomalies in higher-form symmetries cause brane partition functions on closed manifolds to vanish due to net background charges or non-trivial anomalous phases, a framework used to derive Freed-Witten-like anomaly cancellation conditions for M5-branes and D3-branes in S-fold backgrounds.
This study systematically evaluates four derivative-free optimization algorithms for minimizing Hartree-Fock-Roothaan energy functionals involving non-integer Slater-type orbitals, demonstrating their effectiveness in handling the challenging, non-convex landscapes of atomic calculations where analytic derivatives are unavailable.
This paper extends a multiscale modeling framework for sea-ice floes by generalizing particle, kinetic, and hydrodynamic models to account for rotational dynamics, nonlinear contact interactions, and environmental forces such as the Coriolis effect and ocean tilt, thereby providing a more comprehensive description of sea-ice rheology.
This paper proves that the integer-colored bands of the non-interacting Hofstadter butterfly persist as quantized Hall conductivity phases in weakly interacting lattice fermion systems, establishing a many-body gap-labeling theorem that holds for both commensurate and incommensurate magnetic fluxes.
This paper proposes a safe-by-design AGI architecture based on closed reentry loops that mathematically guarantee the emergence of self-models and unprogrammed goal-directed behavior while encoding goals as immutable non-textual vectors, supported by machine-verified proofs, a polynomial-time integrated information measure, and full industrial-scale implementations.
This paper introduces a universal algebraic framework for finite-dimensional open quantum systems that reformulates the Lindblad equation using a closed algebra of Hermitian operators, thereby revealing the richer structure of dissipative dynamics compared to unitary evolution while significantly reducing computational costs through efficient recursion relations and model-independent parametrizations.
This paper establishes sharp -linear estimates for Carleson--Sjölin oscillatory integral operators with arbitrary separated frequency scales and resolves the Burq--Gérard--Tzvetkov problem by proving log-free endpoint bilinear spectral cluster estimates on closed three-dimensional Riemannian manifolds.
This paper employs the nonlinear steepest descent method within a Riemann-Hilbert framework to derive the long-time asymptotic behavior of the defocusing nonlinear Schrödinger equation with step-like initial data, revealing that the solution in the first two transition regions is governed by Painlevé III-type formulas while the third region exhibits collisionless shock dynamics described by Riemann theta functions.
This paper introduces a wave-particle decomposition framework for kinetic relaxation equations that partitions the distribution function into a wave component and a collisionless particle component based on a local evolution timescale, yielding a unified, asymptotic-preserving numerical system that seamlessly adapts across the entire Knudsen spectrum from continuum to rarefied regimes.