Quantum-classical transition in nonlinear dynamical systems.
Viewed as approximations to quantum mechanics, classical evolutions can violate the positive semidefiniteness of the density matrix. The nature of the violation suggests a classification of dynamical systems based on classical-quantum correspondence; we show that this can be used to identify when environmental interaction (decoherence) will be unsuccessful in inducing the quantum-classical transition. In particular, the late-time Wigner function can become positive without any corresponding approach to classical dynamics. In the light of these results, we emphasize key issues relevant for experiments studying the quantum-classical transition.
Habib
Salman
S
T-8, Theoretical Division, MS B285, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
Jacobs
Kurt
K
Mabuchi
Hideo
H
Ryne
Robert
R
Shizume
Kosuke
K
Sundaram
Bala
B