# Dephasing and Decoherence in Open Quantum Systems: A Dyson's Equation Approach

Abstract (Summary)

In this work, the Dyson’s equation formalism is outlined and applied to several open
quantum systems. These systems are composed of a core, quantum-mechanical set of
discrete states and several continua, representing macroscopic systems. The macroscopic
systems introduce decoherence, as well as allowing the total particle number in the system
to change. Dyson’s equation, an expansion in terms of proper self-energy terms, is derived.
The hybridization of two quantum levels is reproduced in this formalism, and it is shown
that decoherence follows naturally when one of the levels is replaced by a continuum.
The work considers three physical systems in detail. The first, quantum dots coupled
in series with two leads, is presented in a realistic two-level model. Dyson’s equation is
used to account for the leads exactly to all orders in perturbation theory, and the time
dynamics of a single electron in the dots is calculated. It is shown that decoherence from
the leads damps the coherent Rabi oscillations of the electron. Several regimes of physical
interest are considered, and it is shown that the difference in couplings of the two leads
plays a central role in the decoherence processes.
The second system relates to the decay-out of superdeformed nuclei. In this case, decoherence
is provided by coupling to the electromagnetic field. Two, three, and infinite-level
models are considered within the discrete system. It is shown that the two-level model
is usually sufficient to describe decay-out for the classic regions of nuclear superdeformation.
Furthermore, a statistical model for the normal-deformed states allows extraction
of parameters of interest to nuclear structure from the two-level model. An explanation
for the universality of decay profiles is also given in that model.
The final system is a proposed small molecular transistor. The Quantum Interference
Effect Transistor is based on a single monocyclic aromatic annulene molecule, with two
leads arranged in the meta configuration. This device is shown to be completely opaque
to charge carriers, due to destructive interference. This coherence effect can be tunably
broken by introducing new paths with a real or imaginary self-energy, and an excellent
molecular transistor is the result.
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School:The University of Arizona

School Location:USA - Arizona

Source Type:Master's Thesis

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