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Title: Geometric Phase for Open Systems
Authors: LEI QIANG
Keywords: quantum entanglement, quantum information, geometric phase
Issue Date: 2-Aug-2007
Citation: LEI QIANG (2007-08-02). Geometric Phase for Open Systems. ScholarBank@NUS Repository.
Abstract: In this thesis, we consider the issue of a geometric phase for systems undergoing non-unitary evolutions. This pertains to systems that are interacting with an environment. Using a relative phase concept, the nature of unitary representations of such evolutions in the combined state space of the system and the environment are shown to be ideal for defining a phase which we term as the geometric phase. It is well known that unitary representations of such evolutions are not unique. Here we show that this non-uniqueness in the representations defines the gauge group and the concomitant parallel transport conditions. In particular we elucidate the nature of these conditions for a class of evolutions that do not lead to level crossings in the Eigen spectrum of the states. We also furnish a gauge-invariant expression for the geometric phase under such maps.
Appears in Collections:Master's Theses (Open)

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