2005/06/30 by R. M. Angelo, Renato M. Angelo · 1 citation
Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Quantum Information and Cryptography #Quantum Mechanics and Applications #quant-ph
paper · pdf · doi:10.1103/physreva.76.052111
published as Phys. Rev. A 76, 052111 (2007). · 10 pages, added references, changed content, accepted in Phys. Rev. A
arxiv created 2007/11/05 · openalex publication_date 2007/11/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 phase-damping 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 quantum-classical correspondence. Moreover, the high-temperature regime is shown to be an additional condition for the quantum-classical transition and, accordingly, a lower bound for the reservoir temperature is derived for our model.