2548 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 derives an explicit formula for the zeta-regularized spectral determinant of Friedrichs Laplacians on singular constant curvature spheres constructed from double triangles, expressing the result in terms of Belyi functions and applying it to Platonic surfaces that serve as stationary points of the determinant.
This paper presents new combinatorial formulae for vector-valued weight functions, also known as off-shell nested Bethe vectors, specifically for evaluation modules over the Yangian .
This paper establishes a structural theorem linking the higher-genus free energy functions of Dubrovin-Zhang hierarchies to the Witten-Kontsevich free energy function, enabling the construction of universal identities for these hierarchies without relying on the geometry of higher-genus moduli spaces.
This paper investigates resonance in two uncoupled oscillators moving within a rectilinear polygon under elastic reflections, establishing a trichotomy for the size of resonant energy sets (empty, singleton, or open) and identifying a special class of potentials, , that allows for an abundance of resonant orbits, analogous to Bertrand's theorem.
This paper establishes a hyperpfaffian framework for computing correlation functions in -ensembles where is an even square integer (), generalizing skew-orthogonal polynomials to construct sparse -vector valued functions that express -point correlations via Vandermonde determinants and hyperpfaffians, with explicit applications to circular ensembles and the case.
This paper presents numerical results and theoretical insights up to 50 qubits to characterize the convergence rates of random quantum circuits to approximate 2-designs, revealing that while most architectures achieve this in logarithmic depth, specific graph topologies like the star graph exhibit a separation between anticoncentration and 2-design formation, and that practical 2-designs can be constructed with significantly fewer layers than previously thought.
This paper establishes that the essential spectrum of the non-Abelian covariant Laplacian on remains if the curvature decays faster than , while demonstrating that this threshold is sharp by constructing a smooth connection with decay where zero enters the essential spectrum.
This paper utilizes the open topological string/spectral theory correspondence to construct exact, analytic generalized eigenfunctions for a class of finite-difference Schrödinger operators arising from supersymmetric Yang-Mills theory, providing a rare example of an exactly solvable spectral problem that describes both bound and resonant states across arbitrary polynomial potentials.
This paper resolves a longstanding open question in quantum information theory by proving that Werner states in arbitrary dimensions are 2-copy distillable if and only if they are 1-copy distillable, marking a significant step toward determining whether all non-positive partial transpose (NPT) states are distillable.
This paper establishes a comprehensive framework for characterizing quantum resources in SU(1,1) systems by constructing covariant quasiprobability distributions on the Poincaré disk, demonstrating that Wigner negativity serves as a definitive witness of nonclassicality for these states, and introducing stellar rank and generalized multipoles as complementary tools for quantifying quantumness.