Correspondence principle for the diffusive dynamics of a quartic oscillator: Deterministic aspects and the role of temperature
Abstract
The correspondence principle is investigated in the framework of deterministic predictions for individual systems. Exact analytical results are obtained for the quantum and Liouvillian dynamics of a nonlinear oscillator coupled to a phasedamping reservoir at a finite temperature. In this context, the time of critical wave function spreading—the Ehrenfest time—emerges as the characteristic time scale within which the concept of deterministic behavior is admissible in physics. A scenario of quasideterminism may then be defined, within which the motion is experimentally indistinguishable from the truly deterministic motion of Newtonian mechanics. Beyond this time scale, predictions for individual systems can be given only statistically and, in this case, it is shown that diffusive decoherence is indeed a necessary ingredient to establish the quantumclassical correspondence. Moreover, the hightemperature regime is shown to be an additional condition for the quantumclassical transition and, accordingly, a lower bound for the reservoir temperature is derived for our model.
 Publication:

Physical Review A
 Pub Date:
 November 2007
 DOI:
 10.1103/PhysRevA.76.052111
 arXiv:
 arXiv:quantph/0506112
 Bibcode:
 2007PhRvA..76e2111A
 Keywords:

 03.65.Yz;
 03.65.Ta;
 03.65.w;
 05.20.Gg;
 Decoherence;
 open systems;
 quantum statistical methods;
 Foundations of quantum mechanics;
 measurement theory;
 Quantum mechanics;
 Classical ensemble theory;
 Quantum Physics
 EPrint:
 10 pages, added references, changed content, accepted in Phys. Rev. A