马尔可夫记忆嵌入于两态自然过程中
摘要：Markovian memory embedded in a binary system is shaping its evolution on the basis of its current state and introduces either clustering or dispersion of binary states. The consequence is directly observed in the lengthening or shortening of the runs of the same binary state and also in the way the proportion of a state within a sequence of state measurements scatters about its true average, which is quantifiable through the Markovian self-transition probabilities. It is shown that the Markovian memory can even imitate the evolution of a random process, regarding the long-term behavior of the frequencies of its binary states. This situation occurs when the associated binary state self-transition probabilities are balanced. To exemplify the behavior of Markovian memory, two natural processes are selected. The first example is studying the preferences of nonhuman troglodytes regarding handedness. The Markovian model in this case assesses the extent of influence two contiguous individuals may have on each other. The other example studies the hindering of the quantum state transitions that rapid state measurements introduce, known as the Quantum Zeno effect (QZE). Based on the current methodology, simulations of the experimentally observed clustering of states allowed for the estimation of the two self-transition probabilities in this quantum system. Through these, one can appreciate how the particular hindering of the evolution of a quantum state may have originated. The aim of this work is to illustrate as merits of the current mathematical approach, its wide range applicability and its potential to provide a variety of information regarding the dynamics of the studied process. 基于当前状态，嵌入在二进制系统中的马尔科夫记忆塑造了它的演化，并引入了二进制状态的聚类或分散。结果直接体现在相同二进制状态的连续性的延长或缩短上，以及状态测量序列中状态的比例如何散布其真实平均值，这可以通过马尔科夫自转移概率来量化。结果表明，马尔科夫记忆甚至可以模拟随机过程的演化，就其二进制状态频率的长期行为而言。当相关的二进制状态自转移概率达到平衡时，就会出现这种情况。为了说明马尔科夫记忆的行为特征，选择了两个自然过程。第一个例子是研究非人类穴居动物对利手性的偏好。在这种情况下，马尔科夫模型评估了相邻个体对彼此可能产生的影响程度。另一个例子研究了快速状态测量引入的量子态转换的阻碍，即量子扎诺效应（QZE）。根据当前的方法，对实验观察到的状态聚类进行模拟，以估计这个量子系统中的两个自转移概率。通过这些，人们可以了解到量子态进化的特定阻碍可能是如何产生的。本工作的目的是说明当前数学方法的优点，它的广泛适用性以及提供有关所研究过程动力学的各种信息的潜力。
作者：Fotini Pallikari and Nikitas Papasimakis
论文ID：0801.3053
分类：Applications
分类简称：stat.AP
提交时间：2008-02-18