Nuclear dynamics nonadiabatic coupling effects

Based on the ab initio theory of complex electronic ground state of superconductors, it can be concluded that e-p coupling in superconductors induces the temperature-dependent electronic structure instability related to fluctuation of analytic critical point (ACP - maximum, minimum or saddle point of dispersion) of some band across FL, which results in breakdown of the adiabatic BOA. When ACP approaches FL, chemical potential Pad is substantially reduced to IJ-antiadilJ-ad > Pantiad < b(o). Under these circumstances the system is stabilized, due to the effect of nuclear dynamics, in the antiadiabatic state at broken symmetry with a gap in one-particle spectrum. Distorted nuclear structure, which is related to couple of nuclei in the phonon mode r that induces transition into antiadiabatic state, has fluxional character. It has been shown that until system remains in antiadiabatic state, nonadiabatic polaron - renormalized phonon interactions are... 

Several other issues are relevant to the discussion of multiple PESs. As previously mentioned, multiple PESs are required for the description of any nonadiabatic effects. Such processes arise in considering relativistic effects and nuclear dynamics. The situation here is more complex than with just the calculation of multiple PESs. Indeed, the accuracy and effort of the calculation of nonadiabatic matrix elements must be assessed against the reliability of the PESs themselves. Furthermore, the issue of coupling of adiabatic surfaces... 

Decoherence is an essential concept appearing in a system in which a quantum subsystem contacts classical subsystem(s) in one way or another. As is widely recognized, the SET cannot describe this dynamics since there is no mechanism in it to switch off the electronic coherence along the nuclear path. The decoherence problem is critically important not only in our nonadiabatic dynamics but in other contemporary science such as spin-Boson dynamics in quantum computation theory and more extensively a quantum theory in open (dissipative) systems [147]. The decoherence problem is also critical to chaos induced by nonadiabatic djmamics [136, 137,182, 453, 454]. Therefore, in the rest of this section, we pay deeper attention to the aspect of the effect of electronic state decoherence strongly coupled with the relevant nuclear motion. A review about the notion of decoherence related to quantum mechanical measmement theory is found in the papers by Rossky et al. [53]. 

Unfortunately, however, the original form of Floquet theorem does not apply to the cases where H is not perfectly periodic. This includes the dynamics under pulsed laser field and/or d3mamics coupled with nuclear motion, which are the cases we are most interested in. In order to apply the Floquet based analyses to such cases, one has to generalize the original formulation. Interestingly, as we will show below, the effects of nonperiodicities can be incorporated in terms of nonadiabatic transitions among Floquet states. 

---