Aharonov Bohm Effect - Impurity Scattering and Phase Coherence

[MSLion]

I'm having difficulties understanding the role of scattering on phase coherence in the Aharonov Bohm Effect.
In particular I am trying to reconcile the following points:

• Inelastic scattering destroys phase coherence and prevents us to see the Aharonov Bohm Effect.
• Elastic scattering does not, but the phase difference will depend on the exact impurity locations.
• Averaging over different mesoscopic samples does not destroy all phase coherence effects. Time-reversed trajectories cause weak localization effect and oscillations in conductance with respect to magnetic field. This effect can bee seen if we align mesoscopic rings in parallel (cylinder).
• Conductance oscillations are not observed in macroscopic samples.

Question:
What happens if I take a MACROscopic ring and cool it down until unelastic scattering becomes neglegible but I still have ring size much larger than mean free path between elastic scattering sites? Will I see the Aharonov Bohm Effect?

Since I think I'm seeing some contradiction here, I believe point 2 is somehow wrong and then the answer to my question would be NO.

However I'm quite confused and would appreciate any help.

 

[M Quack]

My best guess is that in macroscopic object you can never completely eliminate inelastic scattering - there is always a finite electrical resistance.

In mesoscopic objects there are few inelastic scattering events, hence the amplitude of the AB effect is slightly reduced. As you increase the size you introduce more inelastic scatterers and the AB amplitude progressively reduces. I cannot see any reason for a sharp transition from one regime to the other.

If this is true, then it would be interesting to observe the AB amplitude in a single crystal sample with extremely high RRR as function of temperature and size.

Note that this is my best guess, after a nice cold beer, and not supported by any experiments or literature research.