Generalised Geometric Phase
- URL: http://arxiv.org/abs/2301.10929v1
- Date: Thu, 26 Jan 2023 04:27:53 GMT
- Title: Generalised Geometric Phase
- Authors: Vivek M. Vyas
- Abstract summary: A generalised notion of geometric phase for pure states is proposed and its physical manifestations are shown.
The generalised geometric phase is found to contribute to the shift in the energy spectrum due perturbation, and to the forward scattering amplitude in a scattering problem.
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- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: A generalised notion of geometric phase for pure states is proposed and its
physical manifestations are shown. An appreciation of fact that the
interference phenomenon also manifests in the average of an observable, allows
us to define the argument of the matrix element of an observable as a
generalised relative phase. This identification naturally paves the way for
defining an operator generalisation of the geometric phase following
Pancharatnam. The notion of natural connection finds an appropriate operator
generalisation, and the generalised geometric phase is indeed found to be the
(an)holonomy of the generalised connection. It is shown that in scenarios
wherein the usual geometric phase is not defined, the generalised geometric
phase manifests as a global phase acquired by a quantum state in course of time
evolution. The generalised geometric phase is found to contribute to the shift
in the energy spectrum due perturbation, and to the forward scattering
amplitude in a scattering problem.
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