Coherent potential approximation models

The coherent potential approximation for a disordered alloy (7,2) provides a satisfactory framework for describing the effect of alloying within two extremes on the one hand, the rigid-band approximation, which supposes that band shapes do not alter upon alloying, and on the other hand, the minimum polarity model, which supposes the electron distribution of the elements forming an alloy to be similar to that in free atoms. 

The coherent potential approximation (1, 2) is a consistent theoretical frame, which unifies the different alloy models. In order to account for changes in the electronic nature of the atoms, the coherent potential approximation for a disordered alloy appears at present to be the best. It has been applied to single- and two-band systems (130a 130c). 

Gyorffy, B.L. (1972). Coherent-potential approximation for a nonoverlapping muffin-tin potential model of random substitutional alloys, Phys. Rev. B 5, 2382-2384. 

In spite of the apparent consistency of the experimental results with calculations based on the t-matrix theory, the question of the validity of the application of this theory to strong-scattering liquid metals and alloys remains. Harris et al. (1978) have approached this question theoretically by means of a coherent-potential approximation displaying a Debye-Waller factor type of temperature dependence. They succeed by means of this strong-scattering model to reproduce, in semiquantitative fashion, the negative dp, /dr for liquid SnCe. 

Each of the semi-classical trajectory surface hopping and quantum wave packet dynamics simulations has its pros and cons. For the semi-classical trajectory surface hopping, the lack of coherence and phase of the nuclei, and total time per trajectory are cons whereas inclusion of all nuclear degrees of freedom, the use of potentials direct from electronic structure theory, the ease of increasing accuracy by running more trajectories, and the ease of visualization of results are pros. For the quantum wave packet dynamics, the complexity of setting up an appropriate model Hamiltonian, use of approximate fitted potentials, and the... 

Section IV is devoted to excitons in a disordered lattice. In the first subsection, restricted to the 2D radiant exciton, we study how the coherent emission is hampered by such disorder as thermal fluctuation, static disorder, or surface annihilation by surface-molecule photodimerization. A sharp transition is shown to take place between coherent emission at low temperature (or weak extended disorder) and incoherent emission of small excitonic coherence domains at high temperature (strong extended disorder). Whereas a mean-field theory correctly deals with the long-range forces involved in emission, these approximations are reviewed and tested on a simple model case the nondipolar triplet naphthalene exciton. The very strong disorder then makes the inclusion of aggregates in the theory compulsory. From all this study, our conclusion is that an effective-medium theory needs an effective interaction as well as an effective potential, as shown by the comparison of our theoretical results with exact numerical calculations, with very satisfactory agreement at all concentrations. Lastly, the 3D case of a dipolar exciton with disorder is discussed qualitatively. 

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