System-bath coupling strength

Despite the differences in the long-time behavior (due to the lower cutoff in the 1 // case), these two examples allow us to generalize to any dephasing spectrum with a monotonically decreasing system-bath coupling strength as a function of frequency. The optimal modulation for such spectra will be an energy-constrained chirped modulation, with modifications due to other spectral characteristics, for example, cutoffs. 

Figure 4.15 Change of linear entropy in units of the system-bath coupling strength obtained by minimization (attempted cooling) and maximization (attempted heating) of A5 under different constraints E = 0,1,100 as a function of the initial p for a bath as shown in Figure 4.14.

This spectral density has a characteristic low-frequency behavior J((o) — rjo), where rj is the usual ohmic viscosity. The system-bath coupling strength can then be measured in terms of the dimensionless Kondo parameter K, and time scale of bath motions is described by a cutoff frequency (o. For many problems in low-temperature physics, this cutoff frequency is taken to be the largest frequency scale in the problem. In the case of electron transfer, the same spectral density with some intermediate value for is most appropriate for a realistic description of... 

Here rjn is a dimensionless parameter representing the system-bath coupling strength for mode n and is a cut-off frequency which determines the bath relaxation time (see Ref. 19 for more details). 

Fig. 8. Diabatic (a) and adiabatic (b) population probability of the S2 state of the pyrazine model coupled to a harmonic bath, for three values of the system-bath coupling strength. Full line isolated conical intersection rj = 0) dotted hne weak system-bath coupling ( 7 = 0.01) dashed line moderate system-bath coupling ( 7 = 0.05).

The system-bath coupling strength can be characterized by the reorganization parameter, which by convention is set to be ... 

The dynamics quantities in the HEOM formalism are a set of well-defined auxiliary density operators (ADOs), (p (r) = 0,1,...,, in which Po(t) = p t) is just the reduced system density operator. The hierarchy construction resolves not just system-bath coupling strengths but, more importantly, also memory time (l/yo) scales. ... 

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