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 establishes the well-posedness, instantaneous separation, and long-time convergence to stationary states for a two-dimensional bulk-surface Cahn--Hilliard model with non-degenerate mobility and singular potentials, utilizing a novel regularity theory for bulk-surface elliptic systems to prove uniqueness and continuous dependence.
This paper establishes that the uniqueness of quantum state purifications up to local unitary transformations is mathematically equivalent to Haag duality (), demonstrating that this uniqueness can fail in infinite-dimensional systems even when local tomography is possible.
This paper establishes a geometric control framework for boundary-catalytic branching processes by utilizing a Steklov spectral problem to determine the critical absorption rates required to balance population growth and achieve a steady state, while identifying a threshold beyond which such control becomes impossible.
This paper extends PrvanoviÄ's coordinate-free formulation of the Einstein connection for almost Hermitian manifolds to almost contact metric manifolds satisfying an -torsion condition, providing explicit torsion formulas and analyzing special cases within the Gray-Hervella classification.
This paper proposes group entropies as a unifying framework that defines universality classes of extensive entropies for strongly correlated systems, successfully deriving consistent thermodynamic laws and demonstrating that black holes naturally exhibit negative specific heat within this formalism.
This paper establishes that finite non-invertible symmetries in 3+1d without topological line operators necessarily act invertibly on local operators, leading to a decomposition of general non-invertible symmetries into invertible actions and gauging interfaces, and deriving necessary conditions for such symmetries to be anomaly-free.
This paper establishes a relationship between HOMFLY-PT and Kauffman polynomials for specific knot classes using Birman-Murakami-Wenzl algebra characters to prove a conjectured correspondence with Harer-Zagier factorisability for 3-strand knots, while demonstrating through 4-strand counterexamples that this correspondence does not hold universally for knots with higher braid indices.
This paper investigates the classical translational dynamics of homonuclear diatomic molecules in a magnetic quadrupole trap, demonstrating through numerical and analytical methods that the system is non-integrable and exhibits chaotic behavior alongside periodic and quasi-periodic trajectories, with specific solutions expressible via Jacobi elliptic functions.
This paper establishes the existence of nonlinear wave operators and proves small-data asymptotic completeness for the Maxwell-Higgs system with scalar potential on subextremal Kerr spacetimes by constructing a gauge-invariant scattering map that relies on a transfer principle from linear estimates, provided the absence of superradiant instability.
This paper generalizes Backhausz and Szegedy's result on the infinite regular tree by proving that the Gaussian wave is the unique typical process with Green's function covariance for any infinite tree of finite cone type satisfying mild expansion, thereby establishing the convergence of local eigenvector distributions to the Gaussian wave for random bipartite biregular graphs and generic configuration models.