Time-of-arrival probabilities and quantum measurements: III Decay of unstable states

Details Time-of-arrival probabilities and quantum measurements: III Decay of unstable states Time-of-arrival probabilities and quantum measurements: III Decay of unstable states

2007-06-17

arxiv.org/abs/0706.2496v2

J. Math. Phys. 49, 022103 (2008)

Physics

Quantum Physics

27 pages, 2 figs--revised version, small changes, references added, version to appear in J. Math. Phys

Scientific paper

10.1063/1.2839920

We study the decay of unstable states by formulating quantum tunneling as a time-of-arrival problem: we determine the detection probability for particles at a detector located a distance L from the tunneling region. For this purpose, we use a Positive-Operator-Valued-Measure (POVM) for the time-of-arrival determined in quant-ph/0509020 [JMP 7, 122106 (2006)]. This only depends on the initial state, the Hamiltonian and the location of the detector. The POVM above provides a well-defined probability density and an unambiguous interpretation of all quantities involved. We demonstrate that the exponential decay only arises if three specific mathematical conditions are met. Their physical content is the following: (i) the decay time is much larger than any microscopic timescale, so that the fine details of the initial state can be ignored, (ii) there is no quantum coherence between the different `attempts' of the particle to traverse the barrier, and (iii) the transmission probability varies little within the momentum spread of the initial state. We also determine the long time limits of the decay probability and we identify regimes, in which the decays have no exponential phase.

Affiliated with

Also associated with

No associations

Rating

Time-of-arrival probabilities and quantum measurements: III Decay of unstable states does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Time-of-arrival probabilities and quantum measurements: III Decay of unstable states, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Time-of-arrival probabilities and quantum measurements: III Decay of unstable states will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-332462