title: Dephasing by a continuous-time random walk process.
abstract: 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.
authors.affiliation: Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan.
authors.forename: Daniel M
authors.initials: DM
authors.lastname: Packwood
authors.forename: Yoshitaka
authors.initials: Y
authors.lastname: Tanimura
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D008956:Models, Chemical; D015233:Models, Statistical; D044367:Phase Transition; D013057:Spectrum Analysis / Q000379:methods*; D013269:Stochastic Processes