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arXiv:hep-th/0208098 · Physica Scripta

Berry’s Phase in Noncommutative Spaces

S. A. Alavi

Published Jan 1, 2003• 12 citations
arXivHTMLPDF

Abstract

We introduce the perturbative aspects of noncommutative quantum mechanics. Then we study Berry's phase in the framework of noncommutative quantum mechanics. The results show deviations from the usual quantum mechanics which depend on the parameter of space/space noncommutativity.
DOI
10.1238/physica.regular.067a00366

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Abstract In this paper we look for the existence of Berry phase in time dependent harmonic oscillators in noncommutative space. Two systems are considered in our study in the noncommutative framework. The first one is a system in which a scale invariant term is present in the Hamiltonian from the beginning, and the second one is a system in which a scale invariant term emerges due to a change of variables from the noncommutative to the commutative ones. We first compute the eigenstates of both the systems using the Lewis invariant approach. We then employ the Lewis invariant technique to obtain the geometric phase under adiabatic approximation. We also calculate the Berry phase explicitly by choosing appropriate forms of the time dependent parameters appearing in the Hamiltonian. Our analysis surprisingly reveals that a scale invariant time reversal symmetry breaking term may not always lead to a non trivial Berry phase.
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