2563 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 resolves the hyperbolic off-center orbit problem for a singular potential by demonstrating that zero-energy trajectories are Euclidean circles orthogonal to the singularity, governed by an symmetry and an inversion duality that extends to quantum mechanics and magnetic classifications on the hyperbolic plane.
This paper investigates how a generalized uncertainty principle (GUP) modifies the Bekenstein entropy bound in (3+1) and (2+1) dimensions via Geroch's process, demonstrating that a negative deformation parameter relaxes the bound while a positive one tightens it, thereby reflecting Planck-scale near-horizon redshift effects.
This paper recasts Dieter Van den Bleeken's physics discussions within the Kontsevich-Soibelman wall-crossing framework by comparing Hesse and attractor flows, introducing their dual counterparts, and demonstrating how these flows transform into one another under -affine structure rotations, thereby suggesting potential applications in Mirror Symmetry.
This paper establishes that the transmission eigenvalues of monitored Haar products converge to a free multiplicative convolution limit, identifying the resulting spectral distribution via an explicit S-transform and deriving its Erlang-type moments to explain polynomials in Beenakker's recursion while characterizing key spectral features like the atom at unity and a real branch point.
This paper introduces the concept of Physically Accessible Decision-Making (PADM) and a corresponding "measurement-access risk frontier" to demonstrate that autonomous scientific control is fundamentally limited by the physical records available to a system, proving that decision uncertainty cannot be eliminated by computation alone without expanding sensory access, tolerating disturbance, or restricting deployment.
This paper presents a constructive QUBO framework for encoding small Module Learning With Errors (MLWE) instances to enable simultaneous recovery of secrets and errors via quantum annealing, while establishing a theoretical link between the optimization landscape's stability and the problem's energy gap, and assessing its scaling limitations on current hardware.
This review paper explores the deep connection between statistical mechanics and analytic number theory by demonstrating how semiclassical methods, particularly the trace formula and periodic orbit theory, can be used to derive the asymptotic behavior and oscillatory patterns of integer partitions, including those involving distinct squares and prime numbers.
This paper investigates the topological dynamics of pullback maps on full shifts over groups, establishing a sharp dichotomy between equicontinuity and cofinite sensitivity based on the periodicity of group elements under the inducing endomorphism, while also characterizing measure-theoretic properties like Bernoulli preservation and strong mixing.
This paper proposes a high-accuracy semi-analytical method based on cylindrical harmonic expansions and Graf's addition theorem to solve the two-dimensional electromagnetic wave scattering problem for arbitrary ensembles of parallel circular cylinders, enabling numerically verified solutions with controlled precision even for densely packed subwavelength configurations.
This paper constructs non-smooth, finite-time blowup Leray-Hopf solutions to the incompressible Navier-Stokes equations on a periodic 3D torus driven by turbulent fluctuations, while demonstrating that the mean value of such weak solutions corresponds to a smooth solution.