Ohmic spectral density

Fig. 3 Absorption spectra of one sample of B850 calculated with different methods for an Ohmic spectral density with / = 3.37 and usc = 0.027 eV. Left Methods with Markov approximation, i.e. Redfield theory with and without secular approximation and TL method. Right TL with and without Markov approximation, TNL and modified Redfield method. (Reproduced from Ref. [37]. Copyright 2006, American Institute of Physics.)...

Here we apply the LAND-map approach to compute of the time dependent average population difference, A t) = az t)), between the spin states of a spin-boson model. Here az = [ 1)(1 — 2)(2 ]. Within the limits of linear response theory, this model describes the dissipative dynamics of a two level system coupled to an environment [59,63-65]. The environment is represented by an infinite set of harmonic oscillators, linearly coupled to the quantum subsystem. The characteristics of the system-bath coupling are completely described by the spectral density J(w). In the following, we shall restrict ourselves to the case of an Ohmic spectral density... 

Note that in contrast to the ohmic friction, the normal mode friction function has memory. The corresponding spectral density of normal modes /(X) (cf. Eq. (49)) decays as X4, in a sense it is much better behaved than the ohmic spectral density J(o>), which increases without bound with u>. Finally, the collective bath mode frequency, fl (cf. Eq. (59)),... 

However, MD simulation performed to data share one common point—they have all independently validated a three-state spin-boson model description of the RC. In effect, the protein environment can be described in terms of a harmonic oscillator bath with an approximately ohmic spectral density (3.4) where w = 165cm The bare three-state Hamiltonian is... 

In effect, we are dealing with a Hamiltonian like Eq. (3.1) with infinitely many states, N = The nearest-neighbor hopping matrix elements are A, and one can apply an external bias e, which induces a drift on the TB particle. In our simulations we have taken an ohmic spectral density (3.4) with a finite cutoff frequency ca. The two transport quantities of interest are the nonlinear mobility... 

Figure 9.30. Kinetics of the photoinduced back ET reaction for (NH3)5Fe"(CN)(Ru) "(CN)5 in water at BOOK with F = 2500cm , — AG = 3900cm and , = 3800cm . Ohmic spectral density with exponential cutoff at 220 cm is assumed for the solvent. Exact enumeration method (dashed) and the transfer matrix path integral approach (solid) are compared with the Golden Rule prediction (dash-dotted). (Reproduced from [132] with permission. Copyright (1998) by the American Institute of Physics.)...

To demonstrate the accuracy of eqn (12.26) together with eqn (12.30) and its boundary condition eqn (12.31), called the quantum Kramers-like theory, we use a symmetric spin-boson model as a concrete system. In this benchmark model, the nuclear vibrational motions are characterized by the Ohmic spectral density ... 

Here, we have used the fact that B+)g = 0 when we make use of the following expression for what is known as the ohmic spectral density ... 

Wang H, Thoss M (2010) From coherent motion to localization II. Dynamics of the spin-boson model with sub-Ohmic spectral density at zero temperature. Chem Phys 370 78-86... 

Effective-mode chain representations of the bath thus converge rigorously, in that the residual bath converges to an Ohmic spectral density. This result will be illustrated in the next section for a realistic spectral density. 

Panels c and d illustrate the sequence of residual spectral densities fff, which clearly tend towards an Ohmic spectral density (with cut-off) as the order of the effective-mode decomposition increases. The cutoff frequency (Or has to be larger than any frequency of interest (i.e., J (o) 0 for m > cor) here, we have chosen (Or = 4,000cm . The quasi-Ohmlc spectral density towards which the successive TJf s converge coincides with the spectral density generated by the Rubin chain model [12,34,39] with mode frequency fitR/v. The convergence of the sequence towards the Rubin limit follows from the limiting behavior —> 2 that can be... 

In reality, the Ohmic property, J co) co can be satisfied only approximately because from (7.80) it follows that dco J a))/a)) has to be finite. A practical definition of Ohmic spectral density is... 

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