Abstract
We generally study whether or not the information of an open quantum system could be totally erased by its surrounding environment in the long time. For a harmonic oscillator coupled to a bath of a spectral density with zero-value regions, we quantitatively present a threshold of system-bath coupling η_{c}, above which the initial information of the system can remains partially as its long time stablization deviates from the usual thermalization. This non-thermal stabilization happens as a non-Markovian effect.
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