Recurrence and decoherence times of quantum states in a measurement process

Phys. Lett A. 180, 244 (1993) (5 pages)

S. S. Mizrahi, M. H. Y. Moussa, D. Otero


We revisit a time-reversible quantum measurement model proposed by Zurek [Phys. Rev. D 24 (1981) 1516;26 (1982) 1862], which, besides the system and measurement apparatus, also involves the environment. Here, we introduce two additional assumptions: (1) The environment is considered thermalized, with all its two-level atoms having the same energy spacing. (2) The eigenvalues of the apparatus-environment interaction are not assumed all the same for the atoms of the environment, instead, the eigenvalues follow an inverse distance power law according to the ''proximity'' of these to the apparatus. We verify that the recurrence time is only sensible to the number of environment atoms (N), while the decoherence time is much more sensible to the temperature than to N. The ratio of these two characteristic times exhibits a behavior (decreasing with inverse power of N) compatible with what is supposed to happen in a measurement process, when the collapse or reduction of the system-apparatus quantum state takes place.