Kubo golden rule

Recently, Larkin et al. (2000) have encountered (in a study of the spin-ladder system Sr(Cui xZnj )203, which falls outside this review, but see sect. 8.3.4) muon spin relaxation functions with too shallow and too broad minima of polarization to be reproduced by Kubo-Toyabe functions. Again, longitudinal field data showed the spin system to be static. These authors used an approach (called Kubo golden rule, KGR), which was originally derived by Kubo (see Kubo 1981 and Yamazaki 1997) to describe their findings. For details we refer to the original papers. The KGR method allows the calculation of the muon spin relaxation function for arbitrary field distributions (if they can be described by arithmetic function). In the spin-ladder compound an exponential field distribution reproduced the data. The approach of Noakes and Kalvius (1997) can be reproduced using KGR. 

Most approaches to describe spin diffusion are based on a perturbation treatment [11]. Abragam [4] applied Fermi s Golden Rule while Suter and Ernst [12] used the perturbation theory in the rotating frame to obtain an estimate for the rate constant. Henrichs and Linder [13] and Kubo and McDowell [14] used the memory-function theory to model the system. The model of fluctuating local fields can also be applied in a Liouville-space description [15],... 

An important achievement of the early theories was the derivation of the exact quantum mechanical expression for the ET rate in the Fermi Golden Rule limit in the linear response regime by Kubo and Toyozawa [4b], Levich and co-workers [20a] and by Ovchinnikov and Ovchinnikova [21], in terms of the dielectric spectral density of the solvent and intramolecular vibrational modes of donor and acceptor complexes. The solvent model was improved to take into account time and space correlation of the polarization fluctuations [20,21]. The importance of high-frequency intramolecular vibrations was fully recognized by Dogonadze and Kuznetsov [22], Efrima and Bixon [23], and by Jortner and co-workers [24,25] and Ulstrup [26]. It was shown that the main role of quantum modes is to effectively reduce the activation energy and thus to increase the reaction rate in the inverted... 

---