Reduction of the Wavepacket: How Long Does it Take?
We show that the “reduction of the wavepacket” caused by the interaction with the environment occurs on a timescale which is typically many orders of magnitude shorter than the relaxation timescale τ. In particular, we show that in a system interacting with a “canonical” heat bath of harmonic oscillators decorrelation timescale of two pieces of the wave-packet separated by N thermal de Broglie wavelengths is approximately τ/N2. Therefore, in the classical limit ℏ → 0 dynamical reversibility (τ → ∞) is compatible with “instantaneous” coherence loss.
KeywordsDensity Matrix Harmonic Oscillator Classical Limit Free Particle Heat Bath
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