Field domain

This state of affairs holds true even if we consider pulsed excitation in the strong-field domain, provided that the excitation involves only a single precursor state l-E)). In order to see this [39], we generalize the perturbation theory expressions of Section, 2.3.3 to the strong-field domain. We recall that the probability of populating a free state em) km) at any given time is given as... 

We consider now the case of dissociation by the net absorption of just one photon, to jjje1 termed one-photon dissociation. As in the weak-field domain (Chapter 3) the (molecule is assumed to dissociate into two fragments as a result of the interaction (with a laser pulse. It is convenient to parametrize the incident electric field [Eq. (1.35) as... 

Unlike the treatment in the weak-field domain, we do not assume that b (t) 1 at all times. Rather, we integrate the bE a continuum coefficients of Eq. (10.3) over, time, while imposing the boundary condition that the continuum states are empty at the start of the process [i.e., bE a(t - —oo) = 0], to obtain... 

Note that the approach introduced below relies exclusively on the computatir nbfi material matrix elements, as in the wealc-field domain. As a result, one need Ms compute these matrix elements once in order to obtain dissociation rates anu ifohj abilities for a variety of pulse configurations and field strengths. i I % ... 

Following our strategy in the weak-field domain (see Chapter 3), we do not obtain. the photodissociation probability by actually following the dynamics for long times. 

Finally, we make a few additional remarks. First, note that a pure number state is a3j= state whose phase 0k is evenly distributed between 0 and 2n. This is a consequence of the commutation relation [3] between Nk and e,0 <. Nevertheless, dipole mafKi w elements calculated between number states are (as all quantum mechanical amplitudes) well-defined complex numbers, and as such they have well-defined phajje j S Thus, the phases of the dipole matrix elements in conjunction with the mode ph f i f/)k [Eq. (12.15)] yield well-defined matter + radiation phases that determine the outcome of the photodissociation process. As in the weak-field domain, if only gJ one incident radiation mode exists then the phase cancels out in the rate expres4<3 [Eq. (12.35)], provided that the RWA [Eqs. (12.44) and (12.45)] is adoptedf However, in complete analogy with the treatment of weak-field control, if we irradh ate the material system with two or more radiation modes then the relative pb between them may have a pronounced effect on the fully interacting state, phase control is possible. 

Our objective to populate exclusively the z th fragment state E, n, q ) can be i realized in the weak-field domain by choosing the pulse shape that defines P (t) [Eq. (13.60)] to satisfy the condition... 

The weak-field control discussed here must be achieved in two steps. First, if necessary to create the cD(f) superposition state of Eq. (13.65). This state k th irradiated with the pulse satisfying Eq. (13.64). This is the essence of the weak fil pump-dump scenario. However, in the strong-field domain these two procei cannot be separated since the factorization of Eq. (13.62) does not hold. In case the control conditions become 1 ... 

In this strong-field regime the bk t) coefficients are embedded in k(E) [see Eq. (13.58)] and are themselves functions of e(f). Hence the problem is inherently nonlinear, necessitating an iterative solution. Nevertheless, the same interference mechanism outlined in the wealc-field domain applies. The only difference is that the pulse-shaping conditions are given implicitly via Eq. (13.66), rather than explicitly via Eq. (13.64), as in the weak-field domain. 

A. Amann, J. Schlesner, A. Wacker, and E. Scholl Self-generated chaotic dynamics of field domains in superlattices, in Proc. 26th International Conference on the Physics of Semiconductors (ICPS-26), Edinburgh 2002, edited by J. H. Davies and A. R. Long (2003). 

When in a non-homogeneous field, the inolc ules in sUch states will eek the stroiiger field domains to lower their energies. The higher excited states still will be localized about the direction opposite to the field. The molecules in such states will be the low-field seekers they will be expelled outside the field. 

The new model can immediately rationalize the differences in reinforcing activity exhibited by some very similar types of CB, discussed earlier. Especially because of the recent results, indicating no significant difference in surface activity and fractal character of their structure. Modern, very sophisticated methods for estimations of both types of surface parameters describe the surface at sub-nanolevel. So one cannot see primary particle space configurations (responsible for differences) in relief of aggregates (e.g., macropores). In simple terms, if the macropores are of appropriate shape and size, for example, very shallow with flat bottom, concentration in the local internal field domain will be much lower. The external forces transferred by the network continuity from the bulk can in this case much easily draw out the dominant amount of chains from macropore connections decrease in the local layer. 

Observation of a lineshape such as G(t) exp (-at least in some part of the line, is a direct signature of 1-D motion. It requires that the interchain couplings be so small that the cutoff frequency is smaller than the linewidth. The latter being commonly on the order of a few 10 rad/s, this sets the maximum value for the interchain hopping rate. In the class of conducting polymers, to our knowledge, such behavior has only been observed in undoped /ra/ij-polyacetylene. It has been evidenced immediately after Fourier transformation of the usual ESR signal in the frequency/field domain [24]. 

Figure 18 Five holograms stored as holes in the electric field domain. By scanning the field, the five holograms can be read out serially, resulting in a movie showing a running jogger. Reproduced by permission of the Society of Photo-Optical Instrumentation Engineers (SPIE) from Wild UP and Renn A (1988) Proceedings of the SPIE. 910 61.

The observed EPR spectrum is found as a Laplace-Fourier transform of the time dependent averaged transverse magnetisation into the frequency of field domain which is calculated according to the following equation ... 

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