Scaling analysis nonlinear transitions

Davidson s (Appendix E) algorithms. A two-dimensional real space representation of the resulting transition density matrices is convenient for an analysis and visualization of each electronic transition and the molecular optical response in terms of excited-state charge distribution and motions of electrons and holes (Section IIC). Finally, the computed vertical excitation energies and transition densities may be used to calculate molecular spectroscopic observables such as transition dipoles, oscillator strengths, linear absorption, and static and frequency-dependent nonlinear response (Appendix F). The overall scaling of these computations does not exceed X in time and in memory (A being the... 

Our focus has been the elucidation of specific features of the model which give rise to the most important aspects of glass transition behavior. Thus time dependence arises naturally from a consideration of the molecular aspects of the overall phenomena involved. The pronounced nonlinearity and asymmetry of behavior result from the structure dependency of the individual retardation times introduced in the model. In fact, our analysis shows that, on a time scale appropriately compensated to take account of structural dependence, non-linearity and asymmetry vanish. The existence of a multiplicity of recovery times in the model leads to memory, which is observed in real systems. 

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