1677 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 the mathematical framework of minimal sufficient Jordan algebras to characterize the interconversion of quantum statistical experiments via positive, trace-preserving maps, demonstrating that equality in data-processing inequalities implies the existence of recovery maps and that dichotomy interconversion is equivalent under positive and decomposable maps.
This paper establishes that discrete harmonic morphisms provide the minimal condition for exact random walk projection during network renormalization, introducing a "harmonic degree" metric to evaluate how well various coarse-graining methods preserve dynamical invariants and revealing that Laplacian renormalization can spontaneously achieve exact dynamical preservation in real-world networks.
This paper provides a structural explanation for the success and failure of the Bethe Ansatz by identifying interaction propagation as the governing mechanism, where exact solvability arises when propagation terminates finitely without encountering structural boundaries, while its breakdown occurs when such boundaries generate irreducible interaction data that prevent finite factorization.
This paper establishes a direct link between statistical mechanics and the Atiyah-Singer index theorem by demonstrating that the partition function of the quantum harmonic oscillator acts as a Chern character for a "virtual physical sheaf," thereby revealing spectral asymmetry and topological structure in bosonic quantum systems.
This paper establishes a Large Deviation Principle and derives exact closed-form limit shapes for -weighted Muttalib--Borodin ensembles of plane partitions by solving a novel constrained Riemann--Hilbert problem, thereby characterizing a macroscopic phase transition, an arctic curve, and a non-universal hard-edge exponent.
This paper presents a mathematical model of an adsorption column that utilizes travelling-wave analysis and singular perturbation theory to rigorously justify a reduced slow-fast system, demonstrating that the resulting concentration profile transitions from downstream cleanliness to upstream saturation and remains robust even for moderate inverse Péclet numbers.
This paper establishes a rigorous theoretical foundation for efficiently approximating the Quantum Fisher Information Matrix (QFIM) in high-dimensional settings by demonstrating that its classical counterpart, averaged over a few random measurement bases, converges rapidly to the QFIM with provable concentration bounds, thereby enabling cost-effective quantum natural gradient methods.
This paper demonstrates that near-inertial Pollard waves modeling the Arctic Ocean's halocline become linearly unstable when their steepness exceeds a specific threshold, a condition determined by the water column's physical properties through a short-wavelength instability analysis.
This paper constructs a unitarily invariant Hermitian matrix ensemble that realizes the eigenvalue statistics of non-intersecting Brownian bridges with arbitrary endpoint multiplicities, enabling the derivation of exact finite- results, a reduction to a single HCIZ integral, and a comparison of angular statistics with spectrally equivalent Gaussian external-field ensembles.
This paper utilizes the algebraic framework of Symmetry Topological Field Theories (SymTFTs) to generalize quantum dimensions for pseudo-Hermitian systems, thereby providing a systematic classification of their renormalization group flows, quantum phase transitions, and associated domain wall problems through established mathematical principles.