Effect of decoherence on the Berry phase

The Berry (geometric) phase is a significant quantum effect which is associated with conical intersections on excited state potential energy surfaces in molecular photophysics.
An observable consequence is that if a wavepacket is split in two and the two parts traverse opposite sides of the conical intersection (CI) then they will interfere destructively when they meet again on the other side of the CI. [An earlier post considers this effect].

An important question is: what happens to this quantum interference in the presence of decoherence due to the environment?

This question is considered in a nice paper
Quantum-classical description of environmental effects on electronic dynamics at conical intersections
Aaron Kelly and Raymond Kapral

To answer the above question they calculate the probability density on the other side of the CI as a function of the distance from the maximum interference point. This is done for a range of different environment [harmonic oscillator bath] parameters. The key figure is below

In the lower left one sees that there is a dip in the probability at Y=0 due to the quantum interference. The minimum is gradually washed out as the ratio of the bath frequency omega_c to the oscillator frequency omega_x [a measure of the timescale of the semi-classical motion of the wavepackets on the potential energy surface].

I thank Aaron Kelly for helping me understand his work.