Quantum Zeno Effect.

[imiyakawa]

Hi, I don't know much about physics but the limited amount of reading I've done on this particular observation (is that what you call it?) is mind boggling.

http://en.wikipedia.org/wiki/Quantum_Zeno_effect

The quantum Zeno effect ... (is) the situation in which an unstable particle, if observed continuously, will never decay. One can nearly ”freeze” the evolution of the system by measuring it frequently enough in its (known) initial state. The meaning of the term has since expanded ...

Wtf? Is this statement 100% accurate? If it is, what are the consequences for us?

 

[imiyakawa]

Does anybody else see the significance of this?

 

[James Leighe]

Yes and No, the chance of it decaying only tends to 0 as the number of observations per unit time tends to infinity (as far as I know).

What significance are you referring to? It is significant in allot of ways and that's pretty vague.

 

[Jon_Trevathan]

I would like call your attention to Charles Seife article titled: “Furtive Glances Trigger Radioactive Decay [Science http://www.sciencemag.org/cgi/content/summary/288/5471/1564a"[/URL]> by Kurizki and Kofman (Nature, 2000). Seife writes as follows:

“Imagine an alpha particle, two protons and two neutrons, lodged inside a much larger, radioactive nucleus. The particle is there because it can't hurdle the nuclear ‘energy barrier’ that holds it in. Sooner or later, though, the particle probably will escape, causing the nucleus to decay. It can do that by tunneling through the barrier, in a strange quantum way. At first, the particle is firmly stuck on one side of the barrier, but as time goes on, it ‘spreads out’ and starts to exist in a ‘superposition’ of bound and free states that puts it, in effect, on both sides of the barrier at the same time.”

“Before tunneling, a particle can take on a certain range of energies; after tunneling, it has another range. A particle can tunnel only if those energy ranges overlap. Energy ranges, however, can change. If you knock a particle by measuring it, for example, the jolt from the photon broadens the range of energies the particle can take on. The faster you repeatedly measure the particle, the broader the range gets. With more energy options to choose from, the particle spends less time in any particular part of its range. Thus, by repeatedly observing a before-tunneling particle, physicists can ensure that it spends almost all its time at energies that don't overlap with after-tunneling energies. The result: no tunneling, and no nuclear decay.”

Peter W. Milonni provided a more technical summary of this research in a article titled "Quantum decay: A watched pot boils quicker" [Nature [URL]http://www.nature.com/nature/journal/v405/n6786/full/405525a0.html"[/URL]405.6786 (June 1, 2000): p.525(2).]. He wrote as follows:

“An unstable state evolves in time into a linear superposition of states. For instance, an excited state of an atom in a vacuum evolves into a superposition of itself and the (stable) states in which the atom is unexcited and has released a photon into the surrounding space. A measurement to determine whether the initial state survives can be formally described as a projection of the superposition back onto the initial state. The quantum Zeno effect can occur when measurements are repeated so rapidly that the time between them is much shorter than the natural lifetime, or 'coherence time', of the state. Coherence times are typically so short that this condition is not satisfied.”

“Kurizki and Kofman realized that the exact opposite can happen. Suppose, they said, your before-tunneling energies and after-tunneling energies don't overlap to begin with. In that case, the particle can't escape. But repeated measurements might broaden the range of before-tunneling energies so that it creeps into the after-tunneling zone, allowing the nucleus to decay. ‘If you do it sufficiently fast, you would see an increase of the decay rate,’…”

As to what distinguishes the Zeno or anti-Zeno effects, Sabrina Maniscalco, et.at., in their paper titled “Zeno and anti–Zeno effects for quantum Brownian motion” ([PLAIN]http://arxiv.org/PS_cache/quant-ph/pdf/0602/0602133v2.pdf"[/URL]) claim that their findings “yields a new physical explanation of the occurrence of either Zeno or anti-Zeno effects for QBM . The eigenstates of the quantum harmonic oscillator are highly nonclassical states. They are not localized, either in position or in momentum, and therefore they are very sensitive to environment induced decoherence. If the average EID in the interval between two measurements, quantified by , is smaller than the Markovian one, quantified by ΔM, then when the system 'restarts' the evolution after each measurement, the effect of EID is again less than in the Markovian case. Essentially the measurements force the system to experience repeatedly an effective EID which is less strong than the Markovian one. In this case the QZE occurs. On the contrary, whenever the average increase of EID in the interval between two measurements is greater than its Markovian value, then the measurements force the system to experience always a stronger decoherence, and hence the system decay is accelerated (AZE).”

Sabrina Maniscalco, et.al., restated this finding in their follow-on paper titled “Measurement-induced manipulation of the quantum-classical border” ([PLAIN]http://arxiv.org/PS_cache/arxiv/pdf/0704/0704.3179v1.pdf"[/URL]) as follows:

“[Where ] ω0 is the frequency of the system oscillator, and r =ωc/ω0. As we have noted already in Refs. [4, 8], the occurrence of Zeno or anti-Zeno effects strongly depends on the value of the parameter r. Values of r smaller than unity indicate that the frequency of the system oscillator is 'detuned' from the spectrum of the reservoir, while values of r greater than unity indicate an overlap between the reservoir frequency spectrum and ω0..”

Also useful is a survey paper by Wayne Itano titled “Perspectives on the quantum Zeno paradox” ([PLAIN]http://arxiv.org/PS_cache/quant-ph/pdf/0612/0612187v1.pdf"[/URL]).

Although I initially looked at the Zeno and anti-Zeno effects in the context of time symmetric quantum mechanics (TSQM), I eventually came to the conclusion that TSQM need not be involved. However, in the paper by Sabrina Maniscalco, et.al., titled “Zeno and anti–Zeno effects for quantum Brownian motion” (Cited above <[PLAIN]http://arxiv.org/PS_cache/quant-ph/pdf/0602/0602133v2.pdf"[/URL]> ), I also found the following statement: “When the QZE occurs, indeed, an initial delocalized state of the harmonic oscillator such as its energy eigenstate remains delocalized for longer times, hence the QZE “moves forward in time” the quantum–classical border. The opposite situation happens when the AZE occurs.” Although I feel the authors intend the “opposite situation” to imply a relative short “forward in time duration”, I have learned to hold my views “very loosely”.

 

[James Leighe]

That's pretty interesting, learn something new every day.