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Figure 8.7 (a) shows the average photon number as a function of N ex for gtint = 22. Instead of the nice straight line above threshold seen in Figure 8.3 for a typical laser, here we have a highly nonlinear curve. The curve of the fluctuations in the photon number, shown in Figure 8.7(b), also has a much richer structure than its laser counterpart in Figure 8.3. Unlike the case of a laser, gtint = 22 corresponds to an impressive coherent quantum evolution where each atom undergoes about three and a half Rabi cycles before exiting the cavity. Figure 8.7(c) and (d) show the average photon number and its fluctuations for the case of a more modest26 gtint = 0.2. As you can see, the photon number curve is still nonlinear. Moreover, although the curve of the fluctuations in the photon number has a single peak in this region, indicating the threshold as its laser counterpart, unlike Figure 8.3, it becomes sub-Poissonian far above threshold (large N ex ).



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The poorly de ned structure of MAO leads to a corresponding lack of understanding of the actual initiating species formed by reaction between MAO and a metallocene. The usual description of these systems shows the initiating species as XXVII (Eq. 8-52), a monometallic species. Bimetallic species such as XXXVIII and XXXIX have also been proposed. The actual initiating species in any polymerization system may be different, depending on the concentrations (both absolute and relative) of metallocene and MAO. The presence of more than one type of initiating species cannot be ruled out, which would mean that metallocenes do not necessarily always act as single-site initiators. The simultaneous presence of more than one type of initiating specis may also result from the presence of more than a single MAO (and corresponding counterion) structure.

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26In a laser the effective gtint is typically still much smaller than the modest value used in Figure 8.7(c) and (d). Using the experimental data published in [611] for a 0.2-mm-thin Nd:YV04 laser crystal, and taking tint to be the lifetime of the lower level of the lasing transition, we find that the effective gtint is about 10- 4 .

8-5g-2

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Oct 31, 2018 · Steps to convert excel document to PDF programmatically: Create a new C# console application project. Install the Syncfusion.ExcelToPdfConverter.WinForms NuGet packages as reference to your .NET Framework application from NuGet.org. Include the following namespaces in the Program.cs file.

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Imagine that technology were so advanced that we could build a micro maser in the optical regime. 27 How could we get it to behave more like a typical laser The answer is that we would have to spoil the nice coherent quantum dynamics by introducing the dissipative processes that are so common in lasers. Among the many dissipative processes, often the most significant is the extremely fast decay of the polarization of the gain medium. This is why we were able to start our discussion on lasers in this chapter with two rate equations (one for the field intensity, the other for the atomic population) rather than three Maxwell-Bloch equations [533] (where the atomic polarization is also accounted for). What would be the dynamics of an optical micro maser if it had only the incoherent decay of the atomic polarization added to its usual features 28 There is a simple way to describe the polarization decay of a two-level atom. First, we just write down the Schrodinger equation in the form of a master equation. Then we add a Lindblad term, which is identical to that introduced in 6 to account for cavity decay except that a must be replaced by the Pauli matrix 0-z (see the recommended reading). Thus, the master equation for a two-level atom interacting with the field in a resonant single-mode cavity, under some dephasing mechanism that damps the atomic polarization, is given by

Other Lewis acids have been considered as alternatives to MAO for two reasons: (1) one might avoid the cost of the large excess of MAO required to activate the metallocene; and (2) simpler systems, which allow isolation of the product(s) from reaction of metallocene and coinitiator, would be useful to obtain a better understanding of metallocene-initiated polymerizations. Boron-based Lewis acids are useful coinitiators for metallocenes [Chen and Marks, 2000; Chen et al., 1998; Pedeutour et al., 2001; Zhou et al., 2001]. Organoboranes such as

tris(penta uorophenyl)borane and organoborates such as trityl tetrakis(penta uorophenyl)borate react with dimethyl metallocenes to produce very active initiating metallocenium borates for ole n polymerization:

i -r;, [H"] + " ,p p,

[Cp2Zr(CH3)] + [(CH3)B(C6F5)3] XL Cp2Zr(CH3)2 + (C6H5)3C +B(C6F5)4 [Cp2Zr(CH3)] + [B(C6F5)4] + (C6H5)3CCH3 XLI

(8.124)

8-56 8-55

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