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Entanglement and the quantum-classical transition

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Jacobsen, SH (2010) Entanglement and the quantum-classical transition. PhD thesis, University of Tasmania.

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Abstract

The ubiquitous theory of quantum mechanics has sparked many controversial
debates about possible interpretations and its place in fundamental physical
theory. Perhaps most sustained of all the questions is the quest for a complete
explanation of the process behind the reduction from quantum to classical phenomena.
This thesis shall examine this question through detailed investigation
of specific models. The models include a careful exposition of quantum entanglement
through the original EPR thought experiment for continuous variables
and its mathematical transcription. The transcription is compared with existing
methods from quantum optics for achieving experimentally verifiable
Bell-type inequality violations, which are commonly interpreted as violations
of locality. In further development of this famous paradox, the mathematical
model is extended to tripartite continuous variable states, and detailed
measures of their violation of locality are presented.
Having carefully examined quantum phenomena by the EPR-paradox and its
extension to tripartite cases, the investigation proceeds by considering the effect
on quantum systems by an environment. This involves a re-examination of
some well-known quantum system-environment models: the spin-~ Spin-Boson
and Kondo models, in which a two-level quantum system interacts with a bath
of bosons or fermions respectively. The technicalities of the interactions are
exposed in intricate detail, with a careful description of the constructive bosonisation
and transformation methods involved. The thorough analysis leads to
a new observation about the elliptic, or fully anisotropic, Kondo model. Importantly,
the re-examination of the detailed structure of fermion-gas impurity
models and their connection to quantum dissipative systems enables a comprehensive
extension of the family of models to include in particular a new
three-level dissipative system. To underline the importance of this model, it
is shown that the model is exactly solvable by admitting a reparametrisation
of the scattering matrix in terms of R-matrices which obey the Yang-Baxter
equation.
The examination of the interaction between the quantum and the classical
concludes with an investigation of entanglement criteria in the systemenvironment
models discussed. A variational Ansatz for the ground state is
used to demonstrate the numerical calculation of entropy expressions for the
three-level systems, while the reynman-Hellmann Theorem is used to give inprinciple
exact results for the entropy corresponding to the specific three-level
model Hamiltonian introduced in this thesis. Throughout we provide several
suggestions for further work, procedures for experimental verification and
practical application.

Item Type: Thesis (PhD)
Keywords: entanglement, quantum, EPR, dissipative systems, spin boson, Fermi gas, quantum optics
Additional Information:

Copyright 2010 the author

Date Deposited: 11 May 2011 06:47
Last Modified: 11 Mar 2016 05:53
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