  We investigate the role of vacuum (zero-point) fluctuations in generating
decoherence in a number of simple models. First we discuss a harmonic
oscillator coupled to a semi-infinite elastic string and discuss the
irreversible nature of such a bath. We investigate the fluctuations in energy
of the oscillator and discuss the trace the oscillator leaves in the bath. Most
of the work deals with two-level systems coupled to a bosonic bath (a
transmission line). For two-level systems with a Hamiltonian that commutes with
the total Hamiltonian (system plus coupling plus bath) the ground state is a
pure state. The energy of the system is a constant of motion. For the general
case, the energy of the two-level system fluctuates, and the ground state is
only partially coherent. A particular realization of such a two level system
consists of a mesoscopic ring with a quantum dot coupled capacitively to a
transmission line. In the presence of an Aharonov-Bohm flux this system
exhibits a persistent current. This current is a measure of the coherence of
the ground state. As a function of the coupling strength the ground state
undergoes a crossover from a state characterized by a time-averaged persistent
current which is much larger than its time-averaged mean squared fluctuations
to a state characterized by a persistent current with an average amplitude that
is much smaller than its mean squared fluctuations.
