连续时间量子步行系统的最陡熵上升解
Steepest Entropy Ascent Solution for a Continuous-Time Quantum Walker
摘要：
我们考虑用最陡熵升（SEA）模型来描述量子系统的非线性热力学演化。最近这一原理被称为热力学第四定律（贝瑞塔吉安保罗）。热力学第四定律：最陡熵上升（The Fourth Law of Thermodynamics：Steepest Entropy Ascent）在这种情况下，存在唯一的全局平衡态，任何其他状态都是由最大熵产生原理驱动的。研究了N个节点的圈图上连续时间量子步行器（CTQW）的SEA演化。SEA解决方案很难通过分析找到。我们提供了一个近似的计划，以找到一个一般的单粒子演化方程的SEA原则，其解决方案产生耗散动力学。我们称这种方法为固定拉格朗日乘子法（FLM）。在布洛赫球表示中，我们发现由布洛赫向量在球本身内跟踪的轨迹。我们已经讨论了量子比特在各种初始条件下的这些轨迹。在CTQW的情况下，也观察到类似的耗散运动，其中概率幅已被用来表征退相干。我们的FLM方案显示出良好的协议与数值结果。正如文中所报道的，在CTQW中，对于低的系统弛豫时间，存在强的离域。
英文摘要：
We consider the steepest entropy ascent (SEA) ansatz to describe the non-linear thermodynamic evolution of a quantum system. Recently this principle has been dubbed the fourth law of thermodynamics (Beretta Gian Paolo. 2020 The fourth law of thermodynamics: steepest entropy ascent). A unique global equilibrium state exists in this context, and any other state is driven by the maximum entropy generation principle towards this equilibrium. We study the SEA evolution of a continuous-time quantum walker (CTQW) on a cycle graph with N nodes. SEA solutions are difficult to find analytically. We provide an approximate scheme to find a general single-particle evolution equation governed by the SEA principle, whose solution produces dissipation dynamics. We call this scheme fixed Lagrange's multiplier (FLM) method. In the Bloch sphere representation, we find trajectories traced out by the Bloch vector within the sphere itself. We have discussed these trajectories under various initial conditions for the case of a qubit. A similar dissipative motion is also observed in the case of CTQW, where probability amplitudes have been used to characterize decoherence. Our FLM scheme shows good agreement with numerical results. As reported in the text, in CTQW, a strong delocalization exists for low system relaxation time.
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