Does Berry phase exist for a system coupled to its environment?

Details Does Berry phase exist for a system coupled to its environment? Does Berry phase exist for a system coupled to its environment?

2001-07-17

arxiv.org/abs/cond-mat/0107359v1

Physics

Condensed Matter

To be published in Proceedings of XXXVIth Rencontres de Moriond (Jan 2001) "Electronic correlations: from Meso- to Nano-physic

Scientific paper

Berry phase was originally defined for systems whose states are separated by finite energy gaps. One might naively expect that a system without a gap cannot have a Berry phase. Despite this we ask whether a Berry phase can be observed in a system which has a continuous spectrum because its coupling to the environment has broadened its energy levels. We find that, contrary to the above naive expectation, there are conditions under which the Berry phase is observable. However it is modified by the presence of the environment and no longer has a simple geometric interpretation. The model system we consider is a spin-half in a slowly rotating magnetic field, with the spin also coupled to a Ohmic environment of harmonic oscillators (spin-boson model). Here we discuss the high-temperature limit of this model. We then interpret our results in terms of a spin under the influence of a classical stochastic field.

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