Riccardo Adami, Maxime Hauray, Claudia Negulescu
Decoherence for a heavy particle interacting with a light one: new
analysis and numerics
(860K, pdf file)
ABSTRACT. We study the dynamics of a
quantum heavy particle undergoing a repulsive interaction with a light
one. The main motivation is the detailed description of the loss of
coherence induced on a quantum system (in our model, the heavy particle) by
the interaction with the environment (the light particle).
The content of the paper is analytical and
numerical.
Concerning the analytical contribution, we show that an approximate description
of the dynamics of the heavy particle can be carried out in two steps: first
comes the interaction, then the free evolution.
In particular, all effects of the interaction can be embodied in the
action of a collision operator
that acts on the initial state of the heavy particle.
With respect to previous analytical results on the same topics, we
turn our focus
from the M{\o}ller wave operator to the full
scattering operator, whose analysis proves to be simpler.
Concerning the numerical contribution,
we exploit the previous analysis to construct an efficient numerical scheme
that turns the original, multiscale, two-body problem in two
one-body problems
which can be solved separately. This leads to a considerable gain in
simulation time. We present and interpret some simulations carried out on specific
one-dimensional systems by using the new scheme.
Finally, we propose a new description of the mechanism of
decoherence induced by scattering: decoherence is produced by
an interference-free bump which arises from the
initial state of the heavy particle immediately after the collision.
We support such a picture by numerical evidence as well as
by an approximation theorem.