Self propagator representation

As an example. Fig. 1 shows the propagator representation of molecular self-diffusion of ethane in beds of zeolite Na,Ca-A with two different crystalhte sizes. Being symmetric in z, for simphcity the propagator is only represented... 

Fig.l Propagator representation of the self-diffusion of ethane in zeolite Na,Ca-A with mean crystallite radii of R = p.m (a) and 0.4 p.m (b). From [57] with permission... 

Autoxidatlon mechanisms. A simplified visual representation of the self-propagating autoxidation cycles of a polymer dotted lines indicate the points in the mechanism where various AOs interfere with the... 

Fig. 1.15 Left propagator for unrestricted self- tained in an experiment, 5(q), plotted semi-diffusion. The propagator P(R, A) is shown for logarithmically over q2. In this representation, increasing encoding times A and becomes the slope of the decaying function is equal to broader with increasing A, while its intensity at (4 jt)2AD, so that the diffusion coefficient D zero displacement is reduced due to the re- can be obtained directly by comparing at least quirement that the area remains normalized to two measurements taken at different values unity. Right signal function as would be ob- of q.

In this section, we describe our model, and give a brief, self-contained account on the equations of the non-equilibrium Green function formalism. This is closely related to the electron and particle-hole propagators, which have been at the heart of Jens electronic structure research [7,8]. For more detailed and more general analysis, see some of the many excellent references [9-15]. We restrict ourselves to the study of stationary transport, and work in energy representation. We assume the existence of a well-defined self-energy. The aim is to solve the Dyson and the Keldysh equations for the electronic Green functions ... 

Fig. 1 (a) Self-energy in diagrammatic representation, (b) Expansion series for the vertex E up to g. Thick solid, thick dashed, and thin dashed lines indicate, respectively, the electron Green s function, the dressed phonon, and the bare phonon propagators... 

Expressing finally the self-energy operator Z in eq.(3.5) in the TDSHF and employing the local representation in eq.(3.6) for the screening propagator, we arrive at the following expression for the matrix elements of I (only the non-HF part)... 

To be self-contained as much as possible we here make a very brief review of our practice in the application of the FSSH scheme A diabatic representation is used for the dynamics of electron wavefunction. The electron wavefunction is propagated coherently on a reference nuclear trajectory throughout the dynamics. The part of density matrix created by the wave-function is utilized to determine the probability for an otherwise classically continuous path to hop from one PES to another within every time interval [t, t + At]. To be more precise, the switching probability is given as... 

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