3366 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 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.
This paper explains the Aharonov-Bohm effect by demonstrating that the confined magnetic field creates a topological puncture in the particle's configuration space, causing the observed phase shift as a consequence of the modified topology rather than direct nonlocal interaction.
This paper establishes that for trigonometric-polynomial potentials with irrational frequencies, every type I energy with a positive Lyapunov exponent satisfying the gap-labelling condition forms the boundary of an open spectral gap, thereby proving the robustness of the "all spectral gaps are open" property for the supercritical almost-Mathieu operator under small perturbations through a novel geometric approach involving monotonicity and global symplectification.
This paper establishes a unified continuum framework linking chiral liquid crystals and chiral magnets to characterize cholesteric fingers (CF-1 and CF-2) as composite meron-based topological solitons, detailing their structural evolution, repulsive or attractive interactions, and thickness-dependent stability under varying anchoring and background conditions.
This paper introduces a novel quantum relative-alpha-entropy that extends Umegaki's relative entropy beyond the traditional f-divergence framework, revealing a fundamentally geometric notion of quantum distinguishability characterized by nonlinear convexity, additivity, and an exact correspondence with classical relative-alpha-entropy via Nussbaum-Szkola distributions.
This paper introduces the Fast Quantised Numerical Method (FQNM), a novel approach that executes conservative dynamics directly through discrete, antisymmetric integer transfer rules on countable states, thereby achieving superior accuracy in high-frequency transport and robustness in nonlinear shock formation while maintaining exact discrete conservation without relying on traditional floating-point approximations.
This paper proposes a Hamiltonian composite theory of gravity derived from local Lorentz gauge symmetry and freely falling frames, demonstrating that it yields an exact black-hole solution, possesses only four physical degrees of freedom for planar gravitational waves, and provides a framework for quantization.
This paper leverages the detectability lemma to develop efficient Gibbs state preparation methods that eliminate Lindbladian simulation overhead for local Hamiltonians and achieve quadratic speedups in spectral gap dependence by combining the lemma with quantum singular value transformation.
Using the Bethe Ansatz, this paper reveals a novel phase between the Kondo and unscreened phases in the non-Hermitian Kondo model, demonstrating that dissipation drives a phase transition characterized by distinct time scales and a generalized Kondo temperature.