论文标题
在有限状态空间上具有变形的时间抗量量子马尔可夫链
Time-inhomogeneous Quantum Markov Chains with Decoherence on Finite State Spaces
论文作者
论文摘要
我们介绍和研究使用参数$ζ\ ge 0 $和DeColeence参数$ 0 \ leq p \ leq 1 $在有限空间及其大规模平衡属性上。在这里，$ζ$类似于退火随机过程中的反温度，而$ p $是量子系统的折叠强度。数值评估表明，如果$ζ$很小，则量子马尔可夫链对所有$ 0 <p \ le 1 $且如果$ζ$大，则它具有所有$ 0 <p \ le 1 $的多个限制分布。在本文中，我们证明了高温区域中的Ergodic属性$ 0 \leζ\ le 1 $。我们希望相变发生在关键点$ζ_C= 1 $。对于连贯的情况，$ p = 0 $，周期性的关键行为也出现在关键点$ζ_O= 2 $。
We introduce and study time-inhomogeneous quantum Markov chains with parameter $ζ\ge 0$ and decoherence parameter $0 \leq p \leq 1$ on finite spaces and their large scale equilibrium properties. Here $ζ$ resembles the inverse temperature in the annealing random process and $p$ is the decoherence strength of the quantum system. Numerical evaluations show that if $ ζ$ is small, then quantum Markov chain is ergodic for all $0 < p \le 1$ and if $ ζ$ is large, then it has multiple limiting distributions for all $0 < p \le 1$. In this paper, we prove the ergodic property in the high temperature region $0 \le ζ\le 1$. We expect that the phase transition occurs at the critical point $ζ_c=1$. For coherence case $p=0$, a critical behavior of periodicity also appears at critical point $ζ_o=2$.
