Year: 2023
Type: preprint
Abstract: An operator generalisation of the notion of geometric phase has been recently proposed purely based on physical grounds. Here we provide a mathematical foundation for its existence, while uncovering new geometrical structures in quantum systems. While probing the average of any observable it is found that a quantum system exhibits different ray spaces and associated fibre bundle structures. The generalised geometric phase is understood as (an)holonomy of a connection over these fibre bundles. The underlying ray spaces in general are found to be pseudo-Kahler manifolds, and its symplectic structure gets manifests as the generalised geometric phase.
Source: arXiv (Cornell University)
Author: Vyas, Vivek M.
Institution: Indian Institute of Information Technology Vadodara
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4390214833