Matrix dressing

Typical applications include primary devv atering of phosphate rock matrix and silica sand products following vv et screening. In ore dressing it is used rnainlv to protect large-diameter thickeners bv scalping out-l-65-mesh material,... 

Coating for nozzles, dressing sticks for grinding wheels. Matrix material for ceramic composites. 1... 

Therefore, we may define the matrix elements of the dressing operator according to... 

The first conclusion we may draw is that the minimal dressing of a Cl matrix (CAS-SDCI in our study) not only ensures the importanty property of size-extensivity, but also improves the absolute values of the yielded energies. This can be stated in all studied cases single bond breaking, two single bond breaking and triple bond breaking. 

Suppose now that we are interested in a given state M that satisfies the condition stated in eq. (2). As we deal just with one eigenvector, i.e., the set of c coefficients, the dressing matrix need not be composed entirely of non-zero elements. In fact, the single state (SC) operator matrix is diagonal [8]. Its elements are calculated for each G Sq as... 

Most of the tin is not extractable from the dressing matrix but a limit test for... 

Flynn and Stoneham [1970] were the first to suggest that diffusion of the light impurity atom is enhanced by symmetrically coupled vibrations. To incorporate this effect, which is called fluctuational barrier preparation, the authors have proposed to take into account the dependence of the tunneling matrix element on displacements of the heavy nuclei. This approach goes beyond the familiar Condon approximation. In this version of phonon-assisted tunneling, the phonon-dressed incoherent transitions are also induced by a suitable reduction in the barrier height via emission or absorption of phonons. 

Complex rotation can be usefully applied also to the case of the interaction of an atom with a time-dependent perturbation. With the Floquet formalism by Shirley [41], it was shown that, for a time-periodic field, the dressed states of the combined atom-field system can be characterized non-perturbatively by the eigenstates of a time-independent, infinite-dimensional matrix. The combination of the Floquet approach with complex rotation, proposed by Chu, Reinhardt, and coworkers [37, 42, 43], permits to account for the field-induced coupling to the continuum in an efficient way. As in the time-independent case, this results in complex eigenvalues (this time to the Floquet Hamiltonian matrix) and again the imaginary parts give the transition rate to the continuum. This combination has since then been successfully used to examine various strong field phenomena a review can be found in Ref. [44]. 

---