Packwood Daniel M, Tanimura Yoshitaka
Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jul;86(1 Pt 1):011130. doi: 10.1103/PhysRevE.86.011130. Epub 2012 Jul 26.
Stochastic treatments of magnetic resonance spectroscopy and optical spectroscopy require evaluations of functions such as (exp(i ∫(0)(t) Q(s)ds)), where t is time, Q(s) is the value of a stochastic process at time s, and the angular brackets denote ensemble averaging. This paper gives an exact evaluation of these functions for the case where Q is a continuous-time random walk process. The continuous-time random walk describes an environment that undergoes slow steplike changes in time. It also has a well-defined Gaussian limit and so allows for non-Gaussian and Gaussian stochastic dynamics to be studied within a single framework. We apply the results to extract qubit-lattice interaction parameters from dephasing data of P-doped Si semiconductors (data collected elsewhere) and to calculate the two-dimensional spectrum of a three-level harmonic oscillator undergoing random frequency modulations.
磁共振光谱学和光学光谱学的随机处理需要对诸如（exp(i ∫(0)(t) Q(s)ds)）这样的函数进行评估，其中t是时间，Q(s)是随机过程在时间s的值，尖括号表示系综平均。本文针对Q为连续时间随机游走过程的情况，给出了这些函数的精确评估。连续时间随机游走描述了一个随时间经历缓慢阶梯状变化的环境。它还具有明确的高斯极限，因此允许在单个框架内研究非高斯和高斯随机动力学。我们将这些结果应用于从P掺杂Si半导体的退相数据（在其他地方收集的数据）中提取量子比特 - 晶格相互作用参数，并计算经历随机频率调制的三能级谐振子的二维光谱。
