Quantum-to-classical transition in a system with mixed classical dynamics

Abstract

We study how decoherence rules the quantum-classical transition of the kicked harmonic oscillator. The system presents classical dynamics that ranges from regular to strong chaotic behavior depending on the amplitude of the kicks. We show that for regular and mixed classical dynamics, and in the presence of noise, the distance between the classical and quantum phase space distributions is proportional to a single parameter χ≡K â.,eff2 â•4 D3â•2, which relates the effective Planck constant, â.,eff, to the kicking strength, K, and the diffusion constant, D. This relation between classical and quantum distributions is valid when χ<1, a case that is always attainable in the semiclassical regime, independent of the value of the strength of noise given by D. Our results extend a recent study performed in the chaotic regime. © 2006 The American Physical Society.