Dephasing constant

That is, Xw( ) has the Lorentzian shape function. The bandwidth is determined by the damping (or dephasing) constant. 

By omitting the pure dephasing processes, which is warranted at low temperatures, the dephasing constant 1) ), in Eq. (III. 19) can be expressed, in terms of the population decay constants of the states v and v , as... 

Figure 38. Absorption spectrum of pyrazine in the energy region of the S1-S2 conical intersection. Shown are (a) quantum mechanical (full line) and semiclassical (dotted line) results for the four-mode model (including a phenomenological dephasing constant of T2 = 30 fs) and (b) the experimental data [271],...

Figure 41. Absorption spectrum for the 24-mode pyrazine model. The full line is the quantum result [277], and the dotted line is the semiclassical result. In both spectra a phenomenological dephasing constant of = 150 fs was used.

Here, for example, a> mk = a)mk — iymk and ymk is the dephasing constant. Since the system is initially prepared in the manifold, the first term in the bracket involving can be removed. In other words,... 

From the above discussion one can see that due to <7 (At) the measurement of y(quantum beat the beat frequency is a>tt while the beat width is approximately dependent on its dephasing constant. From Eq. (4.53) it can be seen that the ultrafast dynamics of population and coherence appears in initial condition, created by the pumping laser. 

It should be noted that due to er(Af)a a the Fourier transform of % (Lorentzian band-shape with the band-width determined by the dephasing constant of different Fourier transform bands are approximately proportional to the FCFs (0aij 0gg 2 (0ai/ 0go) 2- For the single displaced oscillator case, for example, I I2 = S e 2S, where S is the Huang-Rhys factor of this mode. 

Here, for simplicity the dephasing constant jfu>iv is ignored. Using the relations... 

To construct a model for the P band, the molecular parameters are adopted from Mathies results vibrational frequencies, the coupling constants, the inhomogeneous broadening, and electronic dephasing constant, etc. A microscopic model should contain these molecular parameters. Since... 

When written with the help of the Tl matrix as in (19), from (20) the OR parameter and other linear response properties are seen to afford singularities where co = coj, just like in the SOS equation (2). Therefore, at and near resonances the solutions of the TDDFT response equations (and response equations derived for other quantum chemical methods) yield diverging results that cannot be compared directly to experimental data. In reality, the excited states are broadened, which may be incorporated in the formalism by introducing dephasing constants 1 such that o, —> ooj — iT j for the excitation frequencies. This would lead to a nonsingular behavior of (20) near the coj where the real and the imaginary part of the response function varies smoothly, as in the broadened scenario at the top of Fig. 1. 

The present study uses a quantum statistical method to show how the time-profile of CARS from molecules in liquids is associated with the inteimolecular dephasing mechanisms. Liouville space Feynman diagrams are used for the development of relevant transitions associated with pmrs of molecules. - The structure of the inteimolecular dephasing constant is clarified to identify the difference between the inteimolecular dephasing constant and intramolecular dephasing constant in Sec.ll. Section III presents the rovibrational interference mechanism. The sub-picosecond decay observed in CARS profile of neat benzene is explained in terms of this mechanism. 

Within the Mtuliiov approximation, the intermolecular dephasing constant associated with the coherence decay between i<->j and i ->j vibrational Raman transitions is expressed in terms of the population decay constant from each state and intermolecular pure dephasing constant as ... 

Here f 3( OniB) represents the interaction Hamiltonian between the molecule at site f (m) and the heat bath mode. From the general structure of the intermolecular pure dephasing constant, the intermolecular dephasing constant for the transition i <- j at f tmd i <- j at site m is expressed... 

When the heat bath modes are different between sites ( and m, these molecules are uncorrelated. In this case, the intermolecular dephasing constant consists of the sum of the intramolecular dephasing constants at the two sites,... 

On is the vibrational Raman transition frequency, and Yn is the vibrational dephasing constant Within the high temperature approximation, Eq.(22) is expressed as... 

In recent years high-resolution photochemical hole-burning has shown to be an important technique to study homogeneous lineshapes of molecules in the condensed phase. Especially the unique possibility of measuring simultaneously the low-temperature linewidth and shift" has added much to our understanding of optical dephasing processes. So far however, the relationship between the observed hole-width and optical dephasing constants was not firmly established. 

Following Cohen-Tannoudji and using the Markoffian approximation we have derived the equations of motion for the off-diagonal elements of the reduced density matrix, which determine the dephasing constant (7 ) and the optical lineshape. The following Redfield-like equations were obtained ... 

The S2 absorption spectrum is displayed in Fig. 15. Panel (a) compares the semiclassical and the quantum result and panel (b) shows the experimental data from Ref. 163. Both theoretical results have been obtained by Fourier transformation of the autocorrelation function. Thereby a phenomenological dephasing constant T2 = 30 fs has been included to reproduce the homogeneous width of the experimental spectrum. The absorption spectrum shows a diffuse S2 band with irregularly spaced structures, which cannot be assigned in terms of normal modes in the S2 state. The... 

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