| Summary: | This dissertation is divided up into two parts, each examining a distinct
theme. The rst part of our work concerns itself with open quantum systems and
the relaxation phenomena arising from the repeated application of an interaction
Hamiltonian on systems composed of quantum harmonic oscillators. For the second
part of our work, we shift gears and investigate the wave propagation in left-handed
media, or materials with simultaneously negative electric permeability and magnetic
permeability . Each of these two parts is complete within its own context.
In the rst part of this dissertation, we introduce a relaxation-generating
model which we use to study the process by which quantum correlations are created when an interaction Hamiltonian is repeatedly applied to bipartite harmonic oscillator
systems for some characteristic time interval . The two important time scales
which enter our results are discussed in detail. We show that the relaxation time
obtained by the application of this repeated interaction scheme is proportional to
both the strength of interaction and to the characteristic time interval . Through
discussing the implications of our model, we show that, for the case where the oscillator
frequencies are equal, the initial Maxwell-Boltzmann distributions of the
uncoupled parts evolve to a new Maxwell-Boltzmann distribution through a series
of transient Maxwell-Boltzmann distributions, or quasi-stationary, non-equilibrium
states. We further analyze the case in which the two oscillator frequencies are unequal
and show how the application of the same model leads to a non-thermal steady
state. The calculations are exact and the results are obtained through an iterative
process, without using perturbation theory.
In the second part of this dissertation, we examine the response of a plane
wave incident on a
at surface of a left-handed material, a medium characterized
by simultaneously negative electric permittivity and magnetic permeability . We
do this by solving Maxwell's equations explicitly. In the literature up to date,
it has been assumed that negative refractive materials are necessarily frequency
dispersive. We propose an alternative to this assumption by suggesting that the
requirement of positive energy density can be relaxed, and discuss the implications
of such a proposal. More speci cally, we show that once negative energy solutions
are accepted, the requirement for frequency dispersion is no longer needed. We
further argue that, for the purposes of discussing left-handed materials, the use of
group velocity as the physically signi cant quantity is misleading, and suggest that
any discussion involving it should be carefully reconsidered. === text
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