The case of escape probability as linear in short time |
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Authors: | A. Marchewka Z. Schuss |
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Affiliation: | 1. 8 Galei Tchelet St., Herzliya, Israel;2. Department of Mathematics, Tel-Aviv University, Ramat-Aviv, Tel-Aviv 69978, Israel |
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Abstract: | 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. |
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Keywords: | Escape probability Short time Boundary layer Quadratic in time Linear in time |
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