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What is the quantum anti-zeno effect?

  1. Apr 8, 2014 #1
    With the help of some kind PF folk I recently comprehended the idea of the quantum zeno effect. The idea now seems reasonably simple - the survival probability for any given quantum state tends to one as measurements of that state tend to infinity (over a given time), as a mathematical consequence of the Schrodinger equation plus Born rule.

    But now I see there's something called the ANTI-zeno effect, where continuous measurement somehow INDUCES state change? I don't see how this could happen since (i) the form of the hamiltonian makes no difference to the above original QZE proof (ii) the hamiltonian operator can be substituted out for any operator and the original QZE proof still holds; and (iii) it seems to have nothing to do with open vs closed systems.

    Can anyone explain in simple terms what brings about the anti-zeno effect?

  2. jcsd
  3. Apr 8, 2014 #2


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    When the measurement is trully continuous, i.e. infinitely fast, then only Zeno effect is possible. But when measurement is not infinitely fast, then more terms in the expansion may be needed, in which case the analysis is more complicated and it may happen that Zeno effect is replaced by an anti-Zeno one. That is a qualitative idea, but quantitatively I am not aware of any simple derivation of the anti-Zeno effect.
  4. Apr 8, 2014 #3
    Hmm that's interesting. Going through the literature I've not found anyone saying that it's to do with the rate of the measurements. Rather, it appears to have something to do with what's being measured. So for example, here it is claimed that it is "near threshold decay processes" that may be accelerated by repeated measurements. I'm not entirely sure what those are.

    In fact here it says:

    "Unlike the quantum Zeno effect, which follows from rather general arguments, the possibility of observing a quantum anti-Zeno effect depends on the details of the system."

    And finally here it says:

    "QZE applies only to a restricted class of quantum decay processes. For many common kinds of 'decay' -- for example, when a radioactive atomic nucleus emits a beta particle, or when an energetic molecule gives out 'fluorescent' light -- frequent measurements help the system make the transition from the initial to the decayed state. The change happens more quickly, in other words."

    --- so something funny is going on here...
  5. Apr 8, 2014 #4
    Actually this one is slightly more clear:

    "In the quantum Zeno effect (QZE) frequent measurements inhibit atomic transitions for a
    closed system. In the quantum anti-Zeno effect (QAZE), atomic decays can be accelerated by frequent measurements, when the observed atom also interacts with a heat bath with some spectral distribution."

    So apparently it's to do with open versus closed systems now?
  6. Apr 8, 2014 #5


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    The anti-Zeno effect certainly does depend on all these details you mention. But if the measurement were really instantaneous (which in reality never is), all these details would not matter and we would have a perfect Zeno effect.
  7. Apr 8, 2014 #6
    Okay so for open or closed systems, perfectly continuous measurement yields QZE, moreover closed plus merely frequent measurement yields (approximate) QZE, ...but open plus merely frequent measurement yields QAZE? Or are the conditions less general than this?
  8. Apr 8, 2014 #7


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    I would say so.
  9. Apr 8, 2014 #8

    Any idea what those conditions are? Or is this not yet known?
  10. Apr 9, 2014 #9


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    At least, this is not (yet) known to me.
  11. Apr 9, 2014 #10
    Well I just found a very nice paper on this:

    http://www.phys.lsu.edu/~amarti9/adfaerf/288. Quantum Zeno and anti-Zeno Effects An Exact Model.pdf

    My mathematical background isn't yet sufficient to fully understand this. Nonetheless, it seems that you're right that continuous measurement never gives QAZE, and always gives QZE. This is suggested by their move from equation (29) to equation (30) where they say "Provided n is not too large we can therefore write (30)" and then (30) illustrates the anti-Zeno effect. I'm not 100% sure, but I THINK they are there agreeing with you that QAZE requires frequent non-continuous measurement.

    Now, what kind of systems must be continuously measured? I think their view is that it depends quite precisely on the level of environmental dissipation exhibited by the measured system. After (30) they say: "The conclusion is that the QZE is characterized by small γt values whereas the AZE is characterized by large γt values." I think y (gamma) is a measure of dissipation, but it's not clear because they don't really define the term. Also not clear why it's multiplied by time. But at any rate, it seems QAZE obtains if (i) a system's level of dissipation is over a specific threshold and (ii) frequent measurements are over some specific threshold of frequency but not continuous.

    If you have any insights do let me know!
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