Damping coefficient, coherent

Coupling to these low-frequency modes (at n < 1) results in localization of the particle in one of the wells (symmetry breaking) at T = 0. This case, requiring special care, is of little importance for chemical systems. In the superohmic case at T = 0 the system reveals weakly damped coherent oscillations characterised by the damping coefficient tls (2-42) but with Aq replaced by A ft-If 1 < n < 2, then there is a cross-over from oscillations to exponential decay, in accordance with our weak-coupling predictions. In the subohmic case the system is completely localized in one of the wells at T = 0 and it exhibits exponential relaxation with the rate In k oc - hcoJksTY ". 

In the superohmic case at 7 = 0, the system exhibits weakly damped coherent oscillations characterized by the damping coefficient rjTLS from (2.44), but with A0 replaced by Aeff. In the region lexponential decay, in accordance with our weak-coupling predictions. 

From this relation it is clear that the coherent SI unit for the damping coefficient <5 and the angular frequency a> is the reciprocal second (s 1). However, the special names neper, Np, and radian, rad (see p.ll and p.72), are used for the units of the dimensionless products St and cot respectively. Similarly the quantities 5 and co may be expressed in the units Np/s and rad/s respectively. Used in this way the neper, Np, and the radian, rad, may both be thought of as special names for the number 1. 

The coherence with the reference spectrum has to be verified on the basis of the comparison with spectral ordinates of the accelerograms, for an equivalent viscous damping coefficient of 5%. 

Figure 5 Solvent suppression pulse sequences based on filtering methods. Method (A) uses a 7, filter to discriminate resonances of solvent and solutes. The difference in molecular diffusion coefficients is used in method (B). is the spin-echo time. (C) Double-quantum filtering COSY, which uses the fact that there is no J-coupling between the two equivalent protons in water molecules and thus it cannot be excited to higher quantum coherence. The PFG pulses in (A) and (B) are used to attenuate radiation damping effects and dephase any transverse magnetization. They are used for the desired coherence selection in (C).

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