Coherent motion, description

The significance of the CEO oscillators may be explained by drawing upon the analogy with the description of vibrational spectroscopy, whereby the coherent motion of various atoms with well-defined amplitude and phase relations are represented by collective nuclear coordinates the normal... 

There is another notion which is also very important for the description of the properties of solids, that of collective excitations . In contrast to quasiparticles, these are bosons, they bear no resemblance to constituent particles of a real system, and they involve collective (that is, coherent) motion of many physical particles. We summarize here the most common quasiparticles and collective excitations encountered in solids ... 

This section begins with a brief description of the basic light-molecule interaction. As already indicated, coherent light pulses excite coherent superpositions of molecular eigenstates, known as wavepackets , and we will give a description of their motion, their coherence properties, and their interplay with the light. Then we will turn to linear and nonlinear spectroscopy, and, finally, to a brief account of coherent control of molecular motion. 

A further important property of a MQC description is the ability to correctly describe the time evolution of the electronic coefficients. A proper description of the electronic phase coherence is expected to be particularly important in the case of multiple curve-crossings that are frequently encountered in bound-state relaxation dynamics [163]. Within the limits of the classical-path approximation, the MPT method naturally accounts for the coherent time evolution of the electronic coefficients (see Fig. 5). This conclusion is also supported by the numerical results for the transient oscillations of the electronic population, which were reproduced quite well by the MFT method. Similarly, it has been shown that the MFT method in general does a good job in reproducing coherent nuclear motion on coupled potential-energy surfaces. 

The question then arises if a convenient mixed quantum-classical description exists, which allows to treat as quantum objects only the (small number of) degrees of freedom whose dynamics cannot be described by classical equations of motion. Apart in the limit of adiabatic dynamics, the question is open and a coherent derivation of a consistent mixed quantum-classical dynamics is still lacking. All the methods proposed so far to derive a quantum-classical dynamics, such as the linearized path integral approach [2,6,7], the coupled Bohmian phase space variables dynamics [3,4,9] or the quantum-classical Li-ouville representation [11,17—19], are based on approximations and typically fail to satisfy some properties that are expected to hold for a consistent mechanics [5,19]. 

A rough, zero-order, estimate of the extent to which a Fermi liquid description would be viable in the normal phase is provided by the scale of given by band calculations. Consider the temperature range Tthermal fluctuations are suffieiently weak to lower the uncertainty on the transverse band wave vector to a range of values l/dj, that is small compared to the size of Brillouin zone. The band wave vector is therefore a good quantum number so the transverse band motion and the curvature of the Fermi surface are coherent. Otherwise, when one has which is large enough for... 

The description of excitation motion outlined in the previous sections assumes completely incoherent nearest neighbor hopping. This was treated in detail because it is the case of widest applicability especially with the materials of interest discussed in the final section. However, it should be noted that in some cases excitons can move coherently over several lattice spacings before being scattered i). For this case the diffusion coefficient is expressed in terms of the group velocity of the exciton v and the time between scattering events r. 

In a series of papers, Nieto and colleagues examined in detail the problem of determining coherent states in general, and for some diatomic potential functions such as the Rosen-Morse, Morse, and Pdschl-Teller potentials (Nieto and Simmons, 1978, 1979 Nieto, 1978). The coherent-state approach is a powerful approach to study classically, i.e., at least intuitively, the energetic behavior of diatomics, and, as the authors suggest, provides the classical description of nuclear motion in diatomics. 

The main body of this volume presents results that have been obtained in dynamical studies of proteins in vacuum, in solution, and in crystals. Because of the intense activity in this area, a selection has been made to provide a representative and coherent view of our present knowledge. Where possible, comparisons with experiment and the functional correlates of the motions are stressed. A description is given of specific experimental areas that are of particular importance for the analysis of dynamics or where the simulation results are providing information essential for the interpretation of the experimental data. We conclude with an outlook for future developments and applications in this exciting field. 

It is possible to investigate the flow structure in bubble column reactors by means of hot wire anemometers. The analysis of the liquid-phase velocity data results in consistent descriptive functions on the turbulent motion. The large-scale structures of these flows are determined by the column diameter, and a coherent circulation cell structure must be taken into account. Further measurements are required to establish quantitative relations between the flow structures and disperging properties of turbulent flows. 

A considerable amount of theoretical work has been done on the lineshape of the EPR absorption under the influence of exciton motion. Haken and Strobl (1967, 1973) developed a stochastic model for the description of energy transfer by excitons that includes both the coherent and incoherent... 

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