Stochastic treatments of magnetic resonance spectroscopy and optical spectroscopy require evaluations of functions such as exp(i0tQ sds), 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.
|ジャーナル||Physical Review E - Statistical, Nonlinear, and Soft Matter Physics|
|出版ステータス||Published - 2012 7 26|
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