1202.5060 (G. A. Levin et al.)

Energy Transport in Closed Quantum Systems    [PDF]

G. A. Levin, W. A. Jones, K. Walczak, K. L. Yerkes

We examine energy transport in an ensemble of closed quantum systems driven
by stochastic perturbations. One can show that the probability and energy
fluxes can be described in terms of quantum advection modes (QAM) associated
with the off-diagonal elements of the density matrix. These QAM play the role
of Landauer channels in a system with discrete energy spectrum and the
eigenfunctions that cannot be described as plane waves. In order to determine
the type of correlations that exist between the direction and magnitudes of
each QAM and the average direction of energy and probability fluxes we have
numerically solved the time-dependent Schr\"{o}dinger equation describing a
single particle trapped in a parabolic potential well which is perturbed by
stochastic 'ripples'. The ripples serve as a localized energy source and are
offset to one side of the potential well. As the result a non-zero net energy
flux flows from one part of the potential well to another across the symmetry
center of the potential. We find that some modes exhibit positive correlation
with the direction of the energy flow. Other modes, that carry a smaller energy
per unit of the probability flux, anticorrelate with the energy flow and thus
provide a backflow of the probability. The overall picture of energy transport
that emerges from our results is very different from the conventional one based
on a system with continuous energy spectrum.

View original: http://arxiv.org/abs/1202.5060