Quantum Zeno Effect and Decoherence

[daisey]

I've read the Quantum Zeno (QZ) Effect is caused by Quantum Decoherence (QD), and that QD is, in general, a representation of the wave-function collapse of a quantum system (the Wikipedia explanation on this is confusing to me, to say the least).

If I understand the QZ Effect correctly, unitary time evolution is suspended for the quantum system undergoing the QZ effect.

An example of the QZ Effect that I am familiar with is an unstable atom which does not decay during observation, which would have otherwise already decayed. It would seem to me the wave function of the atom in this example, while under observation, is still intact and has not yet "collapsed", correct? If my understanding here is correct, what then does QD have to do with the QZ Effect? QD seems to involve wave-function collapse, while a system undergoing the QZ effect, there is no wave-function collapse.

What am I missing here?

 

[Ken G]

I'm not sure what you mean by "still intact"-- a collapsed wave function is still a wave function, so it's still intact. The observation causes decoherence of a particular kind, which destroys correlations between the different eigenstates of that measurement (that's basically what a measurement is). Now if the wavefunction is already an eigenstate of the measurement (such as "non-decayed"), but it is not stationary (not an energy eigenstate), then in the absence of measurement, it will develop nonzero amplitudes for the other eigenstates of the measurement. But this takes time, as per the Schroedinger equation. However, if the eigenstate of the measurement is constantly being observed, so constantly decohered, then there is no time to develop those other amplitudes-- the wavefunction is continuously collapsed back to the original eigenstate of the measurement. This constant collapse defeats the time evolution of the Schroedinger equation as it would normally apply to the isolated subsystem-- the coupling to a larger measuring system is what causes, via decoherence, the original eigenstate to be preserved indefinitely.

 

[daisey]

Ken, Thanks for the reply and your patience. I'm not a student of physics. I just read books in my spare time. Some some of these concepts are a little hard for me to grasp.

...a collapsed wave function is still a wave function, so it's still intact.

Wow. That makes sense. The books I've read that talked about, and tried to explain wave function collapse, I don't think ever mentioned that after collapse, the wave function still exists.

The observation causes decoherence of a particular kind, which destroys correlations between the different eigenstates of that measurement (that's basically what a measurement is). Now if the wavefunction is already an eigenstate of the measurement (such as "non-decayed"), but it is not stationary (not an energy eigenstate), then in the absence of measurement, it will develop nonzero amplitudes for the other eigenstates of the measurement.

From reading your response, I think my difficulty understanding the relationship between decoherence and the Zeno effect has to do with the term 'eigenstate'. I get the impression from a Wikipedia article on the term that an item possesses an eigenstate only when the state of the object (ex. position or momentum) is know to some degree. And generally a state is not known until after observation, correct? So how can an observation destroy something (the eigenstate) that does not exist until after observation?

 

[Ken G]

I get the impression from a Wikipedia article on the term that an item possesses an eigenstate only when the state of the object (ex. position or momentum) is know to some degree. And generally a state is not known until after observation, correct? So how can an observation destroy something (the eigenstate) that does not exist until after observation?

Each measurement yields an eigenstate of the measurement, but the outcome can change, thus "destroying" the original state. The idea is that the system might be known originally to be in some state (an eigenstate of some measurement, let's say), but let's say this eigenstate is not "stationary"-- it is not an eigenstate of the Hamiltonian (it does not have a definite energy). This means the state will evolve, and in time will no longer be an eigenstate of the original measurement. So subsequent measurements will not have to yield the same result as the original measurement, the probabilities will change in predictable ways. But the Zeno effect says that it will have to yield the same as the original measurement if the measurement is constantly happening-- there's just no time to evolve to something that is not an eigenstate of the measurement, regardless of what the time evolution is trying to change.