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Fractional decay in the spontaneous emission of a two-level system
Hiroki Nakabayashi, Hayato Kinkawa, Takano Taira, Naomichi Hatano·December 15, 2025
Quantum Physics
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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 $D$ and the exponent $n$ of the energy dispersion $|\vec{k}|^n$ of the environment in the form $1-αt^{2-D/n}$ in the short-time and in the form $αt^{D/n-2}$ 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.