3383 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 a rigorous axiomatic framework that identifies the Fubini-Study metric as the unique canonical distance on projective Hilbert spaces and unifies various quantum information measures through principles of invariance, sensitivity, and contextuality.
This paper demonstrates that while generalized Bopp shifts and Darboux canonicalizations provide linear transformations between noncommutative and ordinary quantum mechanical operators, they do not establish unitary equivalence between the two theories because they correspond to distinct irreducible representations of the underlying nilpotent Lie group that cannot be mapped to one another.
This paper introduces and analyzes the fundamental properties of Banach and separable Orlicz-type spaces defined by nonlocal convolution integral functionals, including the characterization of their duals and illustrative examples.
This paper constructs stationary coherent states concentrated on Lissajous figures for isotropic and anisotropic harmonic oscillators by projecting products of ordinary coherent states onto degenerate subspaces, thereby clarifying phase singularities, linking probability current laminar flow to quantum interference, and providing a rigorous definition of vortex states that resolves to known SU(2) coherent states in the isotropic limit.
This paper extends previous findings on qutrit quantum channels by demonstrating the existence of channels with arbitrarily long minimal synchronizing words, thereby contrasting with the bounds suggested by Černý's conjecture for finite automata.
This paper demonstrates that integrable autonomous partial difference equations admit special solutions governed by non-autonomous ordinary difference equations derived from the Bäcklund transformations of the third and sixth Painlevé equations and the Garnier system in two variables.
This paper establishes that the expectation of multipartite observables formed from sums of local self-adjoint contractions exceeds the product state threshold only when accompanied by a quantifiable amount of total correlation, a relationship derived from the parity structure of the observable's square and bounded by pairwise defect weights.
This paper demonstrates that color symmetry is preserved at high temperatures in the Potts spin glass model with three or more colors using the second moment method, while also proving that unbalanced configurations are exponentially rare for the two-color case at all temperatures due to gauge symmetry.
This paper reformulates and generalizes the equilibrium hyperforce sum rule and the BBGKY hierarchy for both Euclidean and periodic systems by demonstrating that they can be derived from the Leibniz rule applied to the pairing of tempered distributions and Schwartz functions.
This paper establishes finite-depth and finite-shot, dimension-free lower bounds on the success probability of sampling optimal solutions for the Constraint-Enhanced Quantum Approximate Optimization Algorithm (CE-QAOA) by demonstrating that restricting cost angles to a harmonic lattice induces a positive Fejér filter effect.