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 utilizes the Wigner phase-space distribution function and various symmetry groups to explain the transition from classical to quantum mechanics, with a specific focus on characterizing coherent and squeezed states of light, their role in generating entanglement, and the decoherence of optical fields.
This paper establishes entropic uncertainty relations for operator frames in Hilbert-Schmidt space, deriving a strengthened Hirschman-Beckner-type bound for mutually unbiased frames and demonstrating its application to Weyl displacement operators and Wigner kernels to extend uncertainty principles from measurement outcomes to operator representations.
This paper demonstrates that the Scarf I potential problem with a specific position-dependent mass can be solved via a point canonical transformation, yielding exactly-solvable rational extensions associated with -Jacobi exceptional orthogonal polynomials and exhibiting a deformed shape invariance property within a supersymmetric framework.
This paper derives an exact scaling law for the record rate of random walks and Lévy flights with small positive drift, showing that the rate vanishes as a power of the drift determined by the step distribution's skewness and stability index, a result obtained via a unified Mellin transform approach that also recovers known results for expected maximums in queueing and diffusion theory.
This paper establishes sufficient conditions based on the Lipschitz constants and dependency structures of functions to ensure that expectations of their sums under Gaussian or symmetric exponential measures are non-zero, thereby enabling efficient computational approximations with applications to volume and integer point statistics in high-dimensional polyhedra.
This paper establishes the log-concavity of ground states for a broad family of discrete 1D Schrödinger operators, including convex potentials with spikes, to derive new spectral gap bounds and extend perturbative tunneling analyses from linear to quadratic potentials within the framework of adiabatic quantum optimization.
This paper presents an analytically invertible framework that enables the exact, closed-form construction of periodic waveguide networks with prescribed transmission profiles by directly mapping target scattering coefficients to specific physical parameters such as bond connections, refractive indices, and gauge phases.
This paper establishes a semi-device-independent protocol for the genuine certification of incompatible quantum instruments by demonstrating that their violation of tight bounds in specific three-party sequential communication tasks provides a quantum advantage over any classical strategy or compatible quantum implementation.
This paper introduces a Lorentzian Gromov-Hausdorff convergence framework based on causal diamonds and the time separation function, establishing pre-compactness theorems for globally hyperbolic spacetimes and demonstrating the stability of timelike sectional curvature bounds along with connections to causal set theory.
This paper extends the concept of dense Matrix-product state (MPS) skeletons from free-fermion models to interacting -state Onsager-integrable chiral clock chains by constructing MPS that form a dense skeleton in gapped regions and serve as exact eigenstates in specific spectral sectors, thereby enabling closed-form calculations of disorder parameters and revealing new excited states through the Onsager algebra.