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Decoherence at absolute zero
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Decoherence at absolute zero
Supurna Sinha?
Raman Research Institute. Bangalore 560 080. India
Abstract
We present an analytical study of the loss of quantum coherence at absolute
zero. Our model consists of a harmonic oscillator coupled to an environment
of harmonic oscillators at absolute zero. We find that for an Ohmic bath,
the offdiagonal elements of the density matrix in the position representation
decay as a power law in time at late times. This slow loss of coherence in the
quantum domain is qualitatively different from the exponential decay observed
in studies of high temperature environments.
I. INTRODUCTION
Quantum mechanics gives an excellent description of the microscopic world. In all experi-
mental situations studied so far, the predictions of quantum theory have been verified with
phenomenal accuracy. However, ever since the theory came into being it has caused a deep
unease among physicists. This dissatisfaction originates from a belief that the foundations
of the theory are infirm, or at best poorly understood. In order to verify the predictions of
quantum mechanics, one has to perform measurements. However, quantum mechanics does
not provide a description of the measuring process itself. Apart from a dynamical descrip-
?E-mail: supurna@rri.res.in
1
tion of the quantum system via Schro?dinger’s equation, one needs to postulate [1] ad hoc
that the state of the system “collapses” into one of the possible classical outcomes selected
by a measuring apparatus. This point of view, which is popularly known as the Copen-
hagen interpretation, explicitly requires the existence of a classical measuring apparatus. It
is clearly unsatisfactory that for its interpretation quantum mechanics needs to rest upon
classical mechanics, which it is supposed to supersede. A more general theory usually sub-
sumes a less general one as for instance, the special theory of relativity contains Newtonian
phy
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