1695 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 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.
This paper demonstrates that while the combination of Hamiltonian evolution and dissipation in unital quantum Markov semigroups can initially violate complete modified logarithmic Sobolev inequalities, exponential relative entropy decay eventually re-emerges at finite timescales, with a rate inversely bounded by the dissipative strength in the regime of "self-restricting noise" where strong damping suppresses noise spreading.
This paper presents a new strategy to rigorously establish an improved upper bound of $Fr < 1.3451$ for the Froude number of irrotational solitary water waves, marking the first analytical improvement over Starr's classical 1947 result by deriving new inequalities for relative horizontal velocity and applying them to bound the bottom velocity beneath the wave crest.
This paper proves that the fast mode dynamics in quantum operator evolution exhibit emergent random matrix universality within the Krylov space recursion method, leading to universal Green's function scaling forms in both chaotic and non-chaotic systems and enabling a new spectral bootstrap technique for approximating spectral functions.
This paper offers a pedagogical introduction to black hole information loss for readers with a background in special relativity and quantum mechanics, arguing that no true paradox exists and that proposals deviating from established theories are inherently contradictory.
This review highlights classical electrostatic principles—such as potentials for balls and hyperellipsoids, equilibrium measures, conformal mappings, and balayage measures—and demonstrates their applications in predicting asymptotic behaviors, particle densities, fluctuation formulas, and gap probabilities within statistical mechanics and random matrix theory.