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.
|Journal||Physical Review E - Statistical, Nonlinear, and Soft Matter Physics|
|Publication status||Published - 2012 Jul 26|
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics