Motion with electrons identified

It was Schrodinger s intention to associate Zitterbewegung with electron spin, but such an assumption would serve simply to clarify one mystery in terms of another. Instead, one could try first to understand the nature of Zitterbewegung within the region identified as the electron. The only substance available to support the periodic motion is space itself and there seems to be two possibilities either space consists of continuous stuff or of compacted particles. Winterberg [68] explored the latter possibility. Wave motion in a continuous aether is probably easier to visualize and needs fewer assumptions. The only postulate is that ponderable matter and its properties represent special configurations of space. Hence flat Euclidean space (-time) in dimensions of any number, is featureless and empty. 

It could be that the break between respiration and photosynthesis in these bacteria is more recent than we think. Cytochrome Ca has been suggested to have a respiratory as well as a photosynthetic role in R. spheroides (S72) and R. capsulata (372a-c) and no alternative respiratory chain has yet been identified in any of the Athiorhodaceae. In some of these organisms a situation may exist as in Fig. 46 with electrons flowing to both from light-excited bacteriochlorophyll and from external donors, and then from c either to an electron-depleted bacteriochlorophyll or to an oxidase molecule. This would account for the observed control mechanism in the purple nonsulfur bacteria. Under aerobic conditions in the dark, bacteriochlorophyll would not be electron-defi.cient, whereas the oxidase would be in its oxidized state and capable of accepting electrons from c. Under anaerobic conditions, electrons would reduce the oxidase, and further electron transfer down that path would be blocked. Light then would promote electrons away from bacteriochlorophyll and set cyclic photophosphorylation in motion. 

We know that, in semiconductors or insulators, valence and conduction bands are separated by some finite energy gap characteristic of the material. When an electron from the valence band gets sufficient energy to overcome the energy gap may be by thermal excitation or absorption of photons, and it goes to conduction band, a hole is left behind. The electron-hole pair so formed is a quasi-particle called exciton. An exciton can move in the crystal whose centre of mass motion is quantized. Different kinds of excitons can be identified in a variety of materials. If the electron-hole bound pair is tightly-bound with distance of electron-hole pair comparable to lattice constant, then it is called Frenkel exciton. On the other hand, one may have an exciton with electron-hole separation... 

Important aspects of the interaction of strong laser fields with molecules can be missed in standard TOF experiments, most notably the population of electronically excited states. However, by studying vibrational excitation, the frequency and dephasing of the vibrational motion can be used to identify the electronic state undergoing the vibrational motion. In some cases, this turns out to be a ground state, and in others, an excited state. Once we have identified an excited state, we are left with the question of how and why the state was populated by the strong field. In one example above (the Ij A state discussed in Sect. 1.3.3), the excited state is formed by the removal of an inner orbital electron, in this case a iru electron. This correlates with the measured angular dependence for the ionization to this state. 

Because the mapping approach treats electronic and nuclear dynamics on the same dynamical footing, its classical limit can be employed to study the phase-space properties of a nonadiabatic system. With this end in mind, we adopt a onemode two-state spin-boson system (Model IVa), which is mapped on a classical system with two degrees of freedom (DoF). Studying various Poincare surfaces of section, a detailed phase-space analysis of the problem is given, showing that the model exhibits mixed classical dynamics [123]. Furthermore, a number of periodic orbits (i.e., solutions of the classical equation of motion that return to their initial conditions) of the nonadiabatic system are identified and discussed [125]. It is shown that these vibronic periodic orbits can be used to analyze the nonadiabatic quantum dynamics [126]. Finally, a three-mode model of nonadiabatic photoisomerization (Model III) is employed to demonstrate the applicability of the concept of vibronic periodic orbits to multidimensional dynamics [127]. 

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