One more theorem on the shorttime regeneration rate

Pavel Exner

TBD mathscidoc:1910.43135

Journal of Mathematical Physics, 30, (11), 2563-2564, 1989.11
Consider an unstable quantum system that has been found undecayed at an instant s and denote by R(t,s) the rate of its regeneration into an original (undecayed) state at a later instant t+s. It is proved that the reduced evolution is a semigroup, i.e., there is no regeneration at all, provided R(t,s)1/2 can be estimated by a sufficiently regular function that is nondecreasing in s and has zero derivative with respect to t at t=0 for every s. This generalizes the theorem of Misra and Sinha [Helv. Phys. Acta 45, 619 (1972)] in a different direction than in a recent paper by Nishioka [J. Math. Phys. 29, 1860 (1988)].
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  title={One more theorem on the shorttime regeneration rate},
  author={Pavel Exner},
  booktitle={Journal of Mathematical Physics},
Pavel Exner. One more theorem on the shorttime regeneration rate. 1989. Vol. 30. In Journal of Mathematical Physics. pp.2563-2564.
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