Perturbation regime

In the perturbative regime one may decompose these coherences into the contribution from the field and a part which is intrinsic to the matter, the response fiinction. For example, note that the expression (i) p [i i)) is not simply an intrinsic fiinction of the molecule it depends on the fiinctional fomi of the field, since does. Flowever, since the dependence on the field is linear it is possible to write as a... 

The simplified theory allows the time-dependent wave function to be calculated rapidly for any specified laser field. However, controlling the dynamics of the charge carriers requires the answer to an inverse question [18-22]. That is, given a specific target or objective, what is the laser field that best drives the system to that objective Several methods have been developed to address this question. This section sketches one method, valid in the weak response (perturbative) regime in which most experiments on semiconductors are performed. 

Then, in the perturbative regime, a control kernel can be constructed as [23,24],... 

The last assumption is very fundamental. It results in time-independent transition probabilities and makes a clean theory possible. It requires that the product of the time scale of the decay time for the tcf (called the correlation time and denoted x ) and the strength of the perturbation (in angular frequency units) has to be much smaller than unity (17-20). This range is sometimes denoted as the Redfield limit or the perturbation regime. 

In figure 7 the FDCS for 3.6 MeV amu Au ++ He collisions with electron energy Ek = 4.0 eV, and momentum transfer q = 1.0 a.u. have been presented with experimental data from Fischer et al. This is a high-perturbation regime as in figure 6. The theoretical data for (a) and (b) was... 

A theoretical description of CC of excited state dynamics using pulse trains in the perturbative regime, as carried out in experiments [63-65], is presented in Ref. [35]. Analytical expressions relating the excited state populations to the pulse train control parameters are derived in Ref. [35] we refer therein for technical details. We focus on the results here. 

From a practical point of view a major disadvantage of the above control schemes is that they have been applied both theoretically and experimentally mostly in the perturbative regime, thus yielding very small amounts of the desired products. However, intense laser fields give high yields and may even be used to modify the excited molecule in such a way as to drive it to the desired final state. 

The relaxation equation derived so far for electrons and nuclei share a common assumption usually called the perturbation regime or Redfield limit [54]. The... 

Figure 1. Snapshots of quantum probabilities, (a) Weak perturbation regime e = 0.05. b) Strong perturbation regime e = 0.2. The other parameters are set as follows E = 0.75, to = 0.3, Ti = 1000/(3ti X 2 ) 0.1036, and cot2 = 0(mod27t).

Figure 5. Results of the semiclassical calculation in the strong perturbation regime. The parameters are the same as in Fig. 1. (a) The critical points are indicated by x. (b) Jif-set...

To date, most applications of TDDFT fall in the regime of linear response. The linear response limit of time-dependent density functional theory will be discussed in Sect. 5.1. After that, in Sect. 5.2, we shall describe the density-functional calculation of higher orders of the density response. For practical applications, approximations of the time-dependent xc potential are needed. In Sect. 6 we shall describe in detail the construction of such approximate functionals. Some exact constraints, which serve as guidelines in the construction, will also be derived in this section. Finally, in Sects. 7 and 8, we will discuss applications of TDDFT within and beyond the perturbative regime. Apart from linear response calculations of the photoabsorbtion spectrum (Sect. 7.1) which, by now, is a mature and widely applied subject, we also describe some very recent developments such as the density functional calculation of excitation energies (Sect. 7.2), van der Waals forces (Sect. 7.3) and atoms in superintense laser pulses (Sect. 8). 

Applications Beyond the Perturbative Regime Atoms in Strong Femto-Second Laser Pulses... 

The laser is assumed to be linearly polarized along the z-axis and, in the non-perturbative regime, is strong enough to be treated semi-classically, so that... 

Dipole selection rules apply for excitation by single photons in the perturbative regime. Selection rules for multiphoton excitation are different (see chapter 9). For excitation by collisions with charged particles or by light beams of high intensity, turned on so fast that the normal conditions of perturbation theory do not apply, then there are no strict selection rules, although various propensity rules may still apply. 

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