Reduction of the Wavepacket: How Long Does it Take?

Abstract

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 $τ/N^2$. Therefore, in the classical limit $\hbar \to 0$ dynamical reversibility $(τ\to \infty)$ is compatible with ``instantaneous'' coherence loss.