The energy of the bosonic bath and the flow of quantum information in local dephasing channels are studied over short and long times in case the distribution of frequency modes of the bosonic bath exhibits a low-frequency gap. The initial conditions consist in special correlations between the qubit and the bosonic bath or are factorized, and involve thermal states of the whole system or of the bath. The low-frequency gap generates damped oscillations of the bath energy around the asymptotic value, for the correlated initial conditions, and induces the open system to alternately loose and gain information, for the factorized initial configurations. The long-time oscillations of the bath energy become regular and the frequency of the oscillations coincides with the upper cut-off frequency of the spectral gap. Regular long-time sequences of intervals are found over which the bath energy increases (decreases), for the correlated initial conditions, and information is lost (gained) by the open system, for the factorized initial configurations, even at different temperatures. This relation is reversed, if compared to the one obtained without the low-frequency gap, and can fail if the spectral density is tailored near the spectral gap according to power laws with odd natural powers.

中文翻译：

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由光谱间隙和特殊初始相关性引起的玻色子浴能量阻尼振荡

在玻色子浴的频率模式分布呈现低频间隙的情况下，对玻色子浴的能量和局部相移通道中的量子信息流进行了短期和长期研究。初始条件包括量子比特和玻色子浴之间的特殊相关性或被分解，并涉及整个系统或浴的热状态。对于相关的初始条件，低频间隙会在渐近值附近产生阻尼振荡，并且对于分解的初始配置，会导致开放系统交替释放和获得信息。浴能的长时间振荡变得有规律，并且振荡频率与光谱间隙的上限截止频率一致。发现了规律的长时间间隔序列，对于相关的初始条件，浴能量增加（减少），而对于分解的初始配置，即使在不同的温度下，开放系统也会丢失（获得）信息。如果与没有低频间隙的情况相比，这种关系是相反的，并且如果根据具有奇数自然功率的幂律在光谱间隙附近调整频谱密度，则可能会失败。