The case of escape probability as linear in short time

We derive rigorously the short-time escape probability of a quantum particle from its compactly supported initial state, which has a discontinuous derivative at the boundary of the support. We show that this probability is linear in time, which seems to be a new result. The novelty of our calculatio...

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Bibliographic Details
Published in:Physics letters. A 2018-02, Vol.382 (7), p.461-463
Main Authors: Marchewka, A., Schuss, Z.
Format: Article
Language:English
Subjects:
Boundary layer
Escape probability
Linear in time
Quadratic in time
Short time
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Summary:We derive rigorously the short-time escape probability of a quantum particle from its compactly supported initial state, which has a discontinuous derivative at the boundary of the support. We show that this probability is linear in time, which seems to be a new result. The novelty of our calculation is the inclusion of the boundary layer of the propagated wave function formed outside the initial support. This result has applications to the decay law of the particle, to the Zeno behaviour, quantum absorption, time of arrival, quantum measurements, and more. •The short-time escape probability of quantum systems is erroneously believed to always be quadratic.•We show, to the contrary, a prototypical example where the escape probability in short time is linear.•This result opens several perspectives on topics such as the Zeno behaviour, the exponential decay, and so on.
ISSN:0375-9601
1873-2429
DOI:10.1016/j.physleta.2017.12.039