Deterministic flows of Order Parameters in Stochastic Processes of Quantum Monte Carlo Method
Deterministic flows of Order Parameters in Stochastic Processes of Quantum Monte Carlo Method
复制标题
量子蒙特卡罗方法随机过程中阶次参数的确定性流
DOI：
10.1088/1742-6596/233/1/012010
复制
发表时间：
2010
期刊：
影响因子：
--
通讯作者：
Jun-ichi Inoue
中科院分区：
文献类型：
--
作者：
Nakajima;K;Minami;T.;Nakauchi;S.;中本;Jun-ichi Inoue
根据量子力学的马尔可夫链蒙特卡罗方法（MCMC）的随机过程，我们解析地导出了无限程（d =∞）维）量子自旋系统中序参量如自发磁化强度的宏观确定性流方程.利用Trotter分解，我们研究了相应的（d+ 1）维经典系统的Glauber型微观态动力学的跃迁几率.在静态近似下，从描述微观规律的主方程得到关于宏观序参量的微分方程。在定常状态下，我们证明了该方程与同一系统平衡态的鞍点方程是一致的。在经典极限下恢复了动力学伊辛模型的方程。我们还检查的有效性的静态近似利用有限尺寸系统的计算机模拟，并讨论了几种可能的扩展我们的方法无序自旋系统的物理力学信息学。特别是，我们将使用我们的程序来评估贝叶斯图像恢复的解码过程。借助动态复制理论（DRT）的概念，我们推导出了图像恢复测度的零温流方程，该方程在时间演化过程中表现出一些“非单调”行为。
In terms of the stochastic process of quantum-mechanical version of Markov chain Monte Carlo method (the MCMC), we analytically derive macroscopically deterministic flow equations of order parameters such as spontaneous magnetization in infinite-range (d (=∞)-dimensional) quantum spin systems. By means of the Trotter decomposition, we consider the transition probability of Glauber-type dynamics of microscopic states for the corresponding (d+ 1)-dimensional classical system. Under the static approximation, differential equations with respect to macroscopic order parameters are explicitly obtained from the master equation that describes the microscopic-law. In the steady state, we show that the equations are identical to the saddle point equations for the equilibrium state of the same system. The equation for the dynamical Ising model is recovered in the classical limit. We also check the validity of the static approximation by making use of computer simulations for finite size systems and discuss several possible extensions of our approach to disordered spin systems for statistical-mechanical informatics. Especially, we shall use our procedure to evaluate the decoding process of Bayesian image restoration. With the assistance of the concept of dynamical replica theory (the DRT), we derive the zero-temperature flow equation of image restoration measure showing some'non-monotonic'behaviour in its time evolution.