3352 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 establishes that the static correlation properties of mixed-state phases in long-range Lindbladian systems, specifically the polynomial decay of mutual and conditional mutual information, arise naturally from dynamical features like rapid mixing and frustration-freeness, thereby extending Markov property results to long-range regimes relevant for experimental platforms.
This paper introduces a simple geometric "South-East" rule algorithm that determines which critical points contribute to the asymptotic evaluation of multidimensional integrals with exponential integrands, thereby eliminating the need for complex flow computations required by traditional Picard-Lefschetz methods and offering a systematic approach to identifying instanton contributions in real-time path integrals.
This paper establishes a Russo-Seymour-Welsh theorem and the box-crossing property for the antiferromagnetic Ising model and other discrete percolation models that lack the Fortuin-Kasteleyn-Ginibre condition of positive association, demonstrating that these fundamental results hold even without positive association.
This paper constructs a new smooth 4-manifold invariant and an embedding into the hyperfinite II₁ factor that induces a Riemannian metric and "Hodge dynamics," demonstrating that the metric satisfies the Riemannian vacuum Einstein equation if and only if its curvature tensor lies in the fixed-point subalgebra of this dynamics, while also classifying these representations through the lens of thermal equilibrium states in algebraic quantum field theory.
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.