Decoherence and the Quantum-Classical Transition in Phase Space

• Main Authors: Davidovich, L, Filho, R L de Matos, Toscano, F
• Format: Conference Proceeding
• Language: English
• ISSN: 0094-243X
• DOI: 10.1063/1.1928864

We investigate how decoherence affects the short-time separation between quantum and classical dynamics for classically chaotic systems, within the framework of a specific model, which corresponds to an ion trapped in a harmonic trap and submitted to non-resonant laser pulses. For a wide range of parameters, the distance between the classical and quantum (Wigner function) phase-space distributions depends on a single parameter that relates an effective Planck constant eff (given by the square of the Lamb-Dicke parameter), the Lyapunov coeffficient, and the diffusion constant. This distance peaks at a time that depends logarithmically on eff, in agreement with previous estimations of the separation time for Hamiltonian systems. Due to the logarithmic dependence, this time may be very small, even for macroscopis sytems, which would seem to imply that quantum behavior should become manifest after a short time scale. We show however that, for 1, the separation remains small, going down with eff2{expression}. In this limit, the concept of separation time does not make sense anymore, and the classical behavior of the system is recovered.