Geometrical phase factor

The development of electronic geometric phase factors is governed by an adiabatic vector potential induced in the nuclear kinetic energy when we extend the Born-Oppenheimer separation to the degenerate pair of states [1, 23-25]. To see how the induced vector potential appears, we consider the family of transformations which diagonalize the excited state electronic coupling in the form... 

The presence of a conical degeneracy at q = 0 between the upper and lower linear Jahn-Teller surfaces of Eq. (2.9) accounts for the occurrence of nontrivial electronic geometric phase factors in this system [1,2, 26],... 

We hope that the studies summarized above will motivate time-resolved interference experiments on Jahn-Teller systems. Half-odd quantum numbers for molecular pseudorotation have been reported in the continuous wave spectra of Na, [47], benzene [48] and sym-triazine [44]. The half-odd quantum numbers are strong evidence for the presence of geometric phase factors. Benzene and sym-triazine have nondegenerate ground states and would therefore be the most obvious choices for phase sensitive measurements of the kind we propose. The 3s E Rydberg state of 5ym-triazine has the simplifying feature of exhibiting Jahn-Teller... 

The geometric phase effect associated with chemical reactions [166] and with the motion of electrons in magnetic fields [167] was generalized in 1984 by Berry [168] to systems which are transported around a loop or circuit C in parameter space. If H is the system s Hamiltonian and R a set of parametric variables on which H depends, he showed that an eigenstate of when the system is transported slowly (i.e., adiabatically) around C, will acquire a geometrical phase factor independent of time, in addition to the familiar... 

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