4 research outputs found
Characteristics of Quantum-Classical Correspondence for Two Interacting Spins
The conditions of quantum-classical correspondence for a system of two
interacting spins are investigated. Differences between quantum expectation
values and classical Liouville averages are examined for both regular and
chaotic dynamics well beyond the short-time regime of narrow states. We find
that quantum-classical differences initially grow exponentially with a
characteristic exponent consistently larger than the largest Lyapunov exponent.
We provide numerical evidence that the time of the break between the quantum
and classical predictions scales as log(), where is
a characteristic system action. However, this log break-time rule applies only
while the quantum-classical deviations are smaller than order hbar. We find
that the quantum observables remain well approximated by classical Liouville
averages over long times even for the chaotic motions of a few
degree-of-freedom system. To obtain this correspondence it is not necessary to
introduce the decoherence effects of a many degree-of-freedom environment.Comment: New introduction, accepted in Phys Rev A (May 2001 issue), 12 latex
figures, 3 ps figure
The delta-function-kicked rotor: Momentum diffusion and the quantum-classical boundary
We investigate the quantum-classical transition in the delta-kicked rotor and
the attainment of the classical limit in terms of measurement-induced
state-localization. It is possible to study the transition by fixing the
environmentally induced disturbance at a sufficiently small value, and
examining the dynamics as the system is made more macroscopic. When the system
action is relatively small, the dynamics is quantum mechanical and when the
system action is sufficiently large there is a transition to classical
behavior. The dynamics of the rotor in the region of transition, characterized
by the late-time momentum diffusion coefficient, can be strikingly different
from both the purely quantum and classical results. Remarkably, the early time
diffusive behavior of the quantum system, even when different from its
classical counterpart, is stabilized by the continuous measurement process.
This shows that such measurements can succeed in extracting essentially quantum
effects. The transition regime studied in this paper is accessible in ongoing
experiments.Comment: 8 pages, 4 figures, revtex4 (revised version contains much more
introductory material