Geometric Phases and Mielnik's Evolution Loops

TL;DR

This paper investigates geometric phases and evolution loops in quantum systems with equally-spaced energy levels, focusing on harmonic oscillator potentials and their coherent states, revealing new insights into their cyclic evolutions.

Contribution

It provides a detailed analysis of geometric phases and evolution loops in systems with equally-spaced spectra, especially generalized oscillator potentials and their coherent states.

Findings

Identification of conditions for evolution loops in such systems

Characterization of geometric phases in generalized oscillator potentials

Analysis of coherent states related to these potentials

Abstract

The cyclic evolutions and associated geometric phases induced by time-independent Hamiltonians are studied for the case when the evolution operator becomes the identity (those processes are called {\it evolution loops}). We make a detailed treatment of systems having equally-spaced energy levels. Special emphasis is made on the potentials which have the same spectrum as the harmonic oscillator potential (the generalized oscillator potentials) and on their recently found coherent states.