1992 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 changing the initial state in Krylov complexity corresponds to a Christoffel transform of the underlying spectral measure, providing a unified framework to analyze state reorganization, amplitude jumps, and complexity finiteness across various quantum systems through orthogonal polynomial recurrences and kernel projections.
This paper introduces differential operators that relate higher-Wronskian-index solutions to lower-index ones, providing an efficient method to classify rational conformal field theory characters and quasi-characters across the Wronskian tower while preserving modular covariance and integrality.
This paper introduces a new class of Laplace operators for quantum graphs within an operator-system framework by identifying a specific inner product that enables an orthogonal projection, thereby extending classical spectral graph theory to the noncommutative setting and revealing connections to quantum information theory.
This paper constructs the bosonic universal character hierarchy based on the Lie algebra , representing its tau functions via ordered exponential operators and deriving its correlation functions as products of universal characters that are inverses of those in the generalized phase model.
This paper derives compact, coordinate-free transformation laws for torsionful Killing-Yano forms under Abelian T-duality, demonstrating the preservation conditions for Killing 1-forms and providing a generalized-geometric interpretation of emergent isometries through explicit applications to various spacetimes including , Schwarzschild, and the Nappi-Witten plane wave.
This paper rigorously proves that systems of hard rods in a one-dimensional harmonic trap possess no additional analytic conserved quantities beyond total energy and center-of-mass energy, while demonstrating that such extra quantities do exist when the rods are reduced to zero-length point particles.
This three-part series establishes a parameter-free, topological classification of multi-field instabilities in granular continua by demonstrating that odd-channel contact networks inherently possess a structural null-mode that drives secular drift via broken time-reversal symmetry, whereas even-channel networks exhibit harmonic confinement, a distinction validated through analytical 1-D spin chain solutions and high-precision numerical upscaling.
This paper demonstrates that the metric completion of the Bender--Brody--Müller Hamiltonian yields a Hilbert space equivalent to with a purely continuous dilation spectrum, thereby proving that the proposed mechanism cannot generate the point-spectrum eigenstates required to represent the Riemann zeros.
This paper investigates methods to enhance the discrimination power of classically simulable measurements by establishing a framework linking them to Wigner-preserving channels, demonstrating that consumable magic resources can improve performance, while proving that neither quantum catalysts nor quantum memories offer any advantage for discriminating states with positive Wigner functions.
This paper introduces a concrete example of a substochastic Markov chain derived from an open Pelikan random map that exhibits a spectrum of infinitely many quasi-stationary distributions with distinct escape rates, while also establishing the existence of unique quasi-ergodic distributions for certain parameters and validating these findings through numerical simulations.