Periodic measurement of a quantum system

Consider a arrangement in a accompaniment A, which is the eigenstate of some altitude operator. Say the arrangement beneath chargeless time change will adulteration with a assertive anticipation into accompaniment B. If abstracts are fabricated periodically, with some bound breach amid anniversary one, at anniversary measurement, the beachcomber action collapses to an eigenstate of the altitude operator. Amid the measurements, the arrangement evolves abroad from this eigenstate into a superposition accompaniment of the states A and B. If the superposition accompaniment is measured, it will afresh collapse, either aback into accompaniment A as in the aboriginal measurement, or abroad into accompaniment B. However, its anticipation of annoyed into accompaniment B, afterwards a actual abbreviate bulk of time t, is proportional to t², back probabilities are proportional to boxlike amplitudes, and amplitudes behave linearly. Thus, in the absolute of a ample amount of abbreviate intervals, with a altitude at the end of every interval, the anticipation of authoritative the alteration to B goes to zero.

According to decoherence theory, the collapse of the beachcomber action is not a discrete, direct event. A "measurement" is agnate to acerb coupling the breakthrough arrangement to the blatant thermal ambiance for a abrupt aeon of time, and connected able coupling is agnate to common "measurement". The time it takes for the beachcomber action to "collapse" is accompanying to the decoherence time of the arrangement if accompanying to the environment. The stronger the coupling is, and the beneath the decoherence time, the faster it will collapse. So in the decoherence picture, a absolute accomplishing of the breakthrough Zeno aftereffect corresponds to the absolute area a breakthrough arrangement is continuously accompanying to the environment, and area that coupling is always strong, and area the "environment" is an always ample antecedent of thermal randomness.