Towards the end of the recent extremely interesting Aharonov-Bohm Jubilee celebration at Tel Aviv University, Sandu Popescu discussed a putative AB-phase acquisition by an electronic wave-packet of finite dimensions, when it is partially or fully circled by a slowly (adiabatically) moving (and point-like) solenoid. Popescu argued from continuity arguments and invoking the adiabatic theorem, that as the solenoid penetrates the wave-packet some level degeneracy must occur, because of which the phase acquisition takes place. I question this conclusion and suggest that in a partial encirclement, the encircled part of the wave-packet acquires the phase and the un-encircled part does not. Thus the final wave-packet differs from the initial one by more than an overall phase. The adiabatic theorem does not apply here, as it does not apply in other cases where more than one relative time scale is involved [1].

The case for a partial phase-acquisition through the breakdown of the adiabatic theorem is strengthened by models of Aharonov and Kaufherr [2], for which changes occur instantaneously (i.e. non-adiabatically).(Their result evoked some lively controversy at the Jubilee.)

[1] R. Englman and T. Vertesi, Phys. Lett. A 353 (2006) 11

[2] Y. Aharonov and T. Kaufherr, Phys. Rev. Lett. 92 (2004) 070404