### Abstract

Stochastic treatments of magnetic resonance spectroscopy and optical spectroscopy require evaluations of functions such as exp(i0tQ _{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.

Original language | English |
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Article number | 011130 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 86 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2012 Jul 26 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics

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## Cite this

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*,

*86*(1), [011130]. https://doi.org/10.1103/PhysRevE.86.011130