Fractional decay in the spontaneous emission of a two-level system

Hiroki Nakabayashi; Hayato Kinkawa; Takano Taira; Naomichi Hatano

Paper

Fractional decay in the spontaneous emission of a two-level system

Abstract

We find that when the environment of a two-level system has an energy spectrum with a lower bound but without an upper one, the survival probability of the spontaneous emission of the two-level system scales with the spatial dimension

and the exponent

of the energy dispersion

of the environment in the form

in the short-time and in the form

in the long-time regime. The former fractional scaling of the survival probability leads to a quantum Zeno effect with a different scaling of the Zeno time.