Porter-Thomas, distribution

Figure 2. Statistics of current for the transmission through the Sinai billiard for T 0. The upper left panel shows the computed distribution for p = 2 together with the Porter-Thomas distribution P(p) (solid curve). In the inset in the same panel the computed wave function statistics f(p) for the real part of ip is compared with a random Gaussian distribution (solid curve). 

Let us emphasize that the Porter-Thomas distribution is here applied to the resonances of the molecular Hamiltonian in the absence of a radiation held. In the case of NO2 mentioned in Section III, the same distribution with v = 1 was applied, by contrast, to the radiative linewidths of the molecular Hamiltonian [5, 6]. 

In order to obtain the frequency function of the amplitudes for a fixed value W one now has to integrate over W the product of the secular behaviour of jj and the Porter-Thomas distribution. The distribution function of the amplitudes for arbitrary values of initial and final energies then follows after a second integration [VER79]... 

The fluctuations in neutron peak intensities arise from the Porter-Thomas distributed beta decay widths to levels in the NE nuclide. In the simplest case only a single state in the GC nuclide can be fed and only one neutron partial wave is significant. The observed levels will be a subset of levels in the NE nuclide and will be distributed in energy following a Wigner distribution. In a typical GC nuclide, however, there will be a number of accessible final states and the delayed neutron spectrum will be a superposition of transitions from several parts of the NE nuclide level structure. 

From the distributions of the decay widths Ti and r2, which for a chaotic dot are given by the Porter-Thomas distribution [Jalabert 1992 Prigodin 1993]... 

The intensity distribution given by (2.17) has been derived12 for real transition amplitudes. It is referred to as the Porter-Thomas distribution,17 and has been extensively studied in nuclear physics. It is the distribution of transition... 

Figure 8.4 Porter-Thomas distribution of state specific rate constants, Eq. (8.15), for v 1, 2,4, 8, and In these plots x = k and (x) = k (Polik et al, 1990b).

Thus, for state-specific decay and the most statistical (or nonseparable) case, a micro-canonical ensemble does not decay exponentially as predicted by RRKM theory. It is worthwhile noting that when v/2 becomes very large, the right-hand side of Eq. (8.24) approaches exp -kt) (Miller, 1988), since lim (1 + xln) " = exp (-x), when n-> °o. Other distributions for P(k), besides the Porter-Thomas distribution, have been considered and all give M(f, E) expressions which are nonexponential (Lu and Hase, 1989b). 

Three-dimensional quantum mechanical calculations have been performed to determine the unimolecular rate constants for the resonances in HOj H + O2 dissociation (Dobbyn et al., 1995). The resonances are not assignable and the fluctuations in the resonance rate constants can be represented by the Porter-Thomas distribution. Equation 8.17. Thus, the unimolecular dissociation of HO2 is apparently statistical... 

The Porter-Thomas distribution for N(t, ), Eq. (8.24), can be inserted into Eq. (8.35) to obtain the Porter-Thomas lifetime distribution ... 

Figure 8.6 Microcanonical pressure-dependent rate constant (normalized to the average microcanonical rate /c(f), as a function of the reduced collision frequency =

The general class of functions used to describe partial widths are the chi-squared distributions with v degrees of freedom, sometimes called the Porter-Thomas distributions when used to describe resonance widths. Porter and Thomas (42) have shown that the statistical model of the nucleus leads to this type of distribution for the partial widths. The chi-squared distribution for the statistical quantity x can be written as... 

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