Kubo-Anderson process

Exercise. Find the explicit solution of a kangaroo process with i (y) = const, and interpret the result ( Kubo-Anderson process the dichotomic Markov process is a special case). 

Figure 1 Two-dimensional contour plots of the log of the Raman-echo correlation function, In Cre(ti, T3), showing the effect of changing the rate of solvent-induced perturbations. All cases give a Raman line with the same FWHM (5 cm-1) and FIDs with similar decay times but give very different Raman echo results, (a) Fast modulation (b) intermediate modulation (A, = 3.32 cm-1, r( = 1.60 ps) (c) slow modulation. Calculations are based on a single Kubo-Anderson process [Equations (7)-(9)].

The standard assumption of Markovian processes (e.g., the Poissonian Kubo-Anderson processes considered here) fails to explain the statistical properties of emission for certain single molecular systems such as quantum dots [21-23]. Instead of the usual Poissonian processes, a power-law process has been found in those systems. For such highly non-Mar-kovian dynamics stationarity is never reached, and hence our approach as well as the Wiener-Khintchine theorem does not apply. This behavior is the topic of our recent work in [104]. 

If we also assume that the vibrational frequency is modulated by a single process, < correlation time of SoXX). In the Kubo-Anderson model (61-63), the frequency correlation decay is taken to be exponential ... 

We will analyze the SM spectra and their fluctuations semiclassically using the stochastic Bloch equation in the limit of a weak laser field. The Kubo-Anderson sudden jump approach [58-61] is used to describe the spectral diffusion process. For several decades, this model has been a useful tool for understanding line shape phenomena, namely, of the average number of counts < > per measurement time T, and has found many applications mostly in ensemble measurements, for example, NMR [60], and nonlinear spectroscopy [62]. More recently, it was applied to model SMS in low-temperature glass systems in order to describe the static properties of line shapes [14-16, 63] and also to model the time-dependent fluctuations of SMS [64-66]. 

In the limit of a weak external field the model Hamiltonian describes the well-known Kubo-Anderson random frequency modulation process whose properties are specified by statistics of Aco -(t) [58-60]. When the fluctuating part of the optical frequency Am - is a two-state random telegraph process, the Hamiltonian describes a SM (or spin of type A) coupled to J bath molecules (or spins of type B), these being two-level systems. Under certain conditions, this Hamiltonian describes a SM interacting with many two-level systems in low-temperature glasses that has been used to analyze SM line shapes [14-16, 63, 65, 66]. 

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