Quasi-ergodic behavior for crossing diabatic potentials

Victor A. Benderskii^1,2, Evgenii V. Vetoshkin¹, and Efim I. Kats^2,3,*

We investigate coherent and incoherent tunneling phenomena in crossing diabatic potentials (Landau - Zener (LZ) level crossing problem). We consider a model of two crossing parabolic diabatic potentials (left (L) and right (R)) with a constant adiabatic (i.e. independent of coordinates and difference of the diabatic potential minima dE_LR) coupling U₁₂. As a result of coupling and level repulsing, we get the asymmetric double-well lower adiabatic potential with a variable shape depending on a continuous parameter b (which describes for b=1 two identical parabolic diabatic potential crossings and in the limit b→∞ one-well and linear diabatic potentials crossing). We show that the doublet structure of levels (generic for double-well potentials) is remained valid as long as the transition matrix element H_LR (tunnel splitting) is smaller than the characteristic inter-level spacings D_R (which, in turn, decreases upon dE_LR increasing). We calculate the non-adiabatic factor, H_LR as a function of U₁₂. In the diabatic limit (U₁₂→∞) H_LR goes to zero while in the adiabatic limit (U₁₂→∞) the tunneling transitions do not depend on the upper potential. In the over-barrier energy region, H_LR is an oscillating function of U₁₂ due to resonances between the states in the lower and upper adiabatic potentials. In the case H_LR < any level from the shallow L-well is coupled by tunneling to several levels in the R-well, and the transitions lose their coherence. The problem is not only of intellectual interest but also of relevance to various molecular systems undergoing conversion of electronic states or isomerization reactions. Our model exhausts all cases practically relevant for spectroscopy of non-rigid molecules, and can explain many of the experimentally observed features.

PACS: 05.45.-a, 72.10.-d