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. 2011 Dec;84(6 Pt 1):061111. doi: 10.1103/PhysRevE.84.061111. Epub 2011 Dec 7.
We consider separately a spin and an oscillator that are coupled to their environment. After a finite interval of random length, the state of the environment changes, and each change causes a random change in the resonance frequency of the spin or vibrational frequency of the oscillator. Mathematically, the evolution of these frequencies is described by a continuous-time random walk. Physically, the stochastic dynamics can be understood as non-Gaussian because the frequency of the system and state of the environment change on comparable time scales. These dynamics are also nonstationary, and so might apply to a nonequilibrium environment. The resonance and vibrational spectra of the spin and oscillator, as well as the ensemble-averaged displacement of the oscillator, are investigated in detail. We observe some distinct non-Gaussian features of the dynamics, such as the narrow, leptokurtic shape of the resonance spectrum of the spin and beating of the average oscillator displacement. The convergence to Gaussian dynamics as changes in the environment occur with increasing frequency is also considered. Among other results, we observe narrowing of the resonance and vibrational lines in the Gaussian limit due to a weakening of the system-environment interaction.
我们分别考虑一个与环境耦合的自旋和一个振子。在一个具有随机长度的有限时间间隔后，环境状态发生变化，每次变化都会导致自旋的共振频率或振子的振动频率发生随机变化。在数学上，这些频率的演化由连续时间随机游走描述。从物理角度来看，由于系统频率和环境状态在可比的时间尺度上变化，所以随机动力学可被理解为非高斯的。这些动力学也是非平稳的，因此可能适用于非平衡环境。我们详细研究了自旋和振子的共振光谱与振动光谱，以及振子的系综平均位移。我们观察到了动力学的一些明显的非高斯特征，比如自旋共振光谱的窄峰、尖峰形状以及平均振子位移的拍频。我们还考虑了随着环境变化频率增加而向高斯动力学的收敛情况。在其他结果中，我们观察到由于系统 - 环境相互作用减弱，在高斯极限下共振线和振动线变窄。
