A quasi-static treatment of multiple phase jumps

A quasi-static, WKB-type treatment accounts well for the surprising phase jumps that are odd multiples of π (1 + 2n)π, found as a molecular system journeys adiabatically in a configuration coordinate plane that contains several points of degeneracies. We show that the number n in the phase jump is an integer close to |n'| that appears in the expression for the complex wavefunction amplitude valid (approximately) for times close to when the phase jump occurs: -δT + 2πθ+πn'sinδT -i[1-πn'cosδT](δT is a shifted and rescaled trajectory-time parameter and θ is a numerical fraction (<1) which depends on the adiabaticity of the motion.) The central quantity n' is local, i.e., depends on the values of the parameters in the Hamiltonian only at the beginning of the trajectory and at the instant of the phase jump