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Re: Aharonov-Bohm Effect



Eric Cordian wrote:
> 
> Could someone (other than Jim Choate) explain the mechanism behind the
> Aharonov-Bohm effect, where a quantum field propagating via two
> distinct paths finds its wavefunction phase shifted by the amount of magnetic
> flux enclosed, even if it is completely shielded from the magnetic field,
> and traverses only regions of space where B=0.

What do you actually want explaining? Although the magnetic field is
zero along the paths traveled (so that electrons never feel the magnetic
field and the Lorentz force that affects a moving charge in one), the
vector
potential field is not, and is different for the two paths. This causes
the
AB-effect. See, for example G.Baym, 'Lectures on Quantum Mechanics'
(Benjamin, NY, 1969) page 77-79.

> This has apparently been experimentally verified,

Yup, one of the best being N.Osakabe et al, Physics Review A, v34, page
815,
(1986).

> and is a leading candidate for reading the state of quantum dots.

I think you have that the wrong way round - the state of Q. dots is
easy to measure, and so if you put a QD in one arm of an Aharonov-Bohm
interferometer, then measuring the state of the dot allows you know
which path an electron took. If you know that, the wavefunction of
the electron collapses to include just one path, so there is no
interference.
Eyal Buks et al demonstrated this last year - as they increased the
sensitivity of the probe to measure the occupancy of the quantum dot,
the Aharonov-Bohm oscillations in what was classical a separate
system died away.

If you want more details, I'll be happy to explain more. Maybe we should
take it off-list, though, as I seem to have accidently included
references and an informed opinion in my reply, rather than a bigoted
rant.

As for relevance, it is left as an exercise for the reader to work out
why it might be useful to in principle measure fluctuations in a
magnetic
field which is heavily screened, and it's application to cryptography
and
privacy.


Tim

--
Tim Griffiths                   [email protected]
Center for Submicron Research   http://tim01.ex.ac.uk
Weizmann Institute of Science   (972)-8-934-2736
Rehovot 76100 Israel

 'I have sat and listened to the arguments of men,
  and I tell you they are shallow movements in space
  tied to reality only by the ego of their minds.' -DF