Delocalized regime

If vG , respectively vGV, then we say that the system is in the localized regime, respectively the delocalized regime. 

We give now a scaling limit result in the strongly delocalized regime under the condition that if(-) decays sufficiently rapidly. One is certainly tempted to conjecture the validity of such a result in the whole class of inter-arrival distributions that we consider and everywhere in T>. We will come back to this issue in the next section (with no definite answer). 

A general consideration on this chapter is that the results presented are sensibly weaker than those in Chapter 2 and Chapter 3 for homogeneous and weakly inhomogeneous models. It is then natural to ask what should we expect to observe in the delocalized regime of disordered models This question is particularly relevant also because weakly inhomogeneous models have been studied as caricatures of disordered models. 

In the strongly delocalized regime, from Theorem 8.6 one can extract the weak convergence statements of Corollary 8.7 for general return time distribution, but only along subsequences. 

Chapter 7 and Chapter 8 deal with the properties of polymer paths. These are sharply different in the locahzed regime (Ch. 7) and in the delocahzed one (Ch. 8). The two chapters are independent and they do not require a detailed knowledge of Ch. 5 and Ch. 6. In fact I beheve that they can even be read directly after Ch. 4, but of comse it may be somewhat reassming knowing that a localized, or delocalized, regime does exist. 

Do we expect this model to be accurate for a dynamics dictated by Tsallis statistics A jump diffusion process that randomly samples the equilibrium canonical Tsallis distribution has been shown to lead to anomalous diffusion and Levy flights in the 5/3 < q < 3 regime. [3] Due to the delocalized nature of the equilibrium distributions, we might find that the microstates of our master equation are not well defined. Even at low temperatures, it may be difficult to identify distinct microstates of the system. The same delocalization can lead to large transition probabilities for states that are not adjacent ill configuration space. This would be a violation of the assumptions of the transition state theory - that once the system crosses the transition state from the reactant microstate it will be deactivated and equilibrated in the product state. Concerted transitions between spatially far-separated states may be common. This would lead to a highly connected master equation where each state is connected to a significant fraction of all other microstates of the system. [9, 10]... 

At very low temperatures, Holstein predicted that the small polaron would move in delocalized levels, the so-called small polaron band. In that case, mobility is expected to increase when temperature decreases. The transition between the hopping and band regimes would occur at a critical temperature T, 0.40. We note, however, that the polaron bandwidth is predicted to be very narrow ( IO Viojo, or lO 4 eV for a typical phonon frequency of 1000 cm-1). It is therefore expected that this band transport mechanism would be easily disturbed by crystal defects. 

In a regime of strong interaction between the chains no optical coupling between the ground slate and the lowest excited state occurs. The absence of coupling, however, has a different origin. Indeed, below 7 A, the LCAO coefficients start to delocalize over the two chains and the wavefunclions become entirely symmetric below 5 A due to an efficient exchange of electrons between the chains. This delocalization of the wavcfunclion is not taken into account in the molecular exciton model, which therefore becomes unreliable at short chain separations. Analysis of the one-electron structure of the complexes indicates that the... 

The MO theory differs greatly from the VB approach and the basic MO theory is an extension of the atomic structure theory to molecular regime. MOs are delocalized over the nuclear framework and have led to equations, which are computationally tractable. At the heart of the MO approach lies the linear combination of atomic orbitals (LCAO) formahsm... 

Figures 3.5 and 3.6 present schematic classification of regimes observable for the A + B —> 0 reaction. We will concentrate in further Chapters of the book mainly on diffusion-controlled kinetics and will discuss very shortly an idea of trap-controlled kinetics [47-49]. Any solids contain preradiation defects which are called electron traps and recombination centres -Fig. 3.7. Under irradiation these traps and centres are filled by electrons and holes respectively. The probability of the electron thermal ionization from a trap obeys the usual Arrhenius law 7 = sexp(-E/(kQT)), where s is the so-called frequency factor and E thermal ionization energy. When the temperature is increased, electrons become delocalized, flight over the conduction band and recombine with holes on the recombination centres. Such...

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