论文标题
中央自旋与有限自旋浴的中心自旋的崩溃和复兴结构
Collapse and revival structure of information backflow for a central spin coupled to a finite spin bath
论文作者
论文摘要
量子动力学的马尔可夫性是由系统和浴室的各种成分决定的开放量子系统的重要特性。除了系统浴的相互作用，浴缸的初始状态等外，浴缸的尺寸在确定量子动力学的马尔可维亚性方面起着至关重要的作用，因为严格的浴缸相关性衰减需要浴缸的无限尺寸。在这项工作中，我们通过考虑一个简单但非平凡的模型来研究有限浴缸在量子动力学的马克维亚度中的作用，其中中央旋转与有限数量的浴缸旋转相结合，并显示中心旋转的动力学是如何从非马克维亚人到浴缸的数量增加的。非马克维亚性的特征是从系统状态的痕量距离方面，信息从浴缸回到系统。我们通过分析痕量距离得出时间的演变，并在信息流中找到周期性的崩溃恢复模式。该现象的基础机制进行了详细研究，并表明，倒塌 - 复兴模式的周期取决于浴缸的数量，系统浴耦合强度和频率失节之间的竞争。当沐浴旋转的数量足够大时，倒塌的复兴结构的周期以及相应的崩溃和复兴时间与浴缸的数量成比例增加，这表征了信息回流如何逐渐衰减浴缸的尺寸。我们还分析了系统托架相互作用强度和频率使信息流的崩溃复兴模式的影响，并获得了存在崩溃的恢复结构的条件。结果通过数值计算说明。
The Markovianity of quantum dynamics is an important property of open quantum systems determined by various ingredients of the system and bath. Apart from the system-bath interaction, the initial state of the bath, etc., the dimension of the bath plays a critical role in determining the Markovianity of quantum dynamics, as a strict decay of the bath correlations requires an infinite dimension for the bath. In this work, we investigate the role of finite bath dimension in the Markovianity of quantum dynamics by considering a simple but nontrivial model in which a central spin is isotropically coupled to a finite number of bath spins, and show how the dynamics of the central spin transits from non-Markovian to Markovian as the number of the bath spins increases. The non-Markovianity is characterized by the information backflow from the bath to the system in terms of the trace distance of the system states. We derive the time evolution of the trace distance analytically, and find periodic collapse-revival patterns in the information flow. The mechanism underlying this phenomenon is investigated in detail, and it shows that the period of the collapse-revival pattern is determined by the competition between the number of the bath spins, the system-bath coupling strength, and the frequency detuning. When the number of bath spins is sufficiently large, the period of the collapse-revival structure as well as the respective collapse and revival times increase in proportion to the number of the bath spins, which characterizes how the information backflow decays with a large dimension of the bath. We also analyze the effect of the system-bath interaction strength and frequency detuning on the collapse-revival patterns of the information flow, and obtain the condition for the existence of the collapse-revival structure. The results are illustrated by numerical computation.
