Wednesday, December 19, 2007

Correspondence Principle

Just finished a paper on the "Correspondence principle and chaos for a macroscopic quantum device". The surprising feature here is that the application of a traditional expression of the correspondence principle is not possible. It needs to be rephrased to something along the lines of:

Consider \hbar fixed (it is) and scale the Hamiltonian so that when compared with the minimum area \hbar/2 in phase space:
  1. the relative motion of the expectation values of the observable become large and
  2. the state vector is localised.
Then, under these circumstances, expectation values of operators will behave like their classical counterparts.

Even then application of this statement is limited by circuit parameters.

I would welcome any observations or constructive criticisms on this result:

http://arxiv.org/abs/0712.3043

3 comments:

Ian said...

It takes awhile to get these blog things going. I'll add you to my list. In any case, your paper looks interesting. I will need to check it out. Have you looked through Frank Schroeck's book on QM in phase space? The late A.S. Eddington once tried to "derive" the exclusion principle from the uncertainty principle in phase space essentially using a Planck cell.

Mark J Everitt said...

Thank you.

I'm not sure about the ability to "derive" the exclusion principle from the uncertainty principle in phase space essentially using a Planck cell but you certainly can use phase space methods to understand it. Here, distributions such as the Wigner function become particularly effective. Wolfgang Schleich's book Quantum Optics in Phase Space is a very good example.

Mark J Everitt said...

now published at:
http://www.iop.org/EJ/abstract/-search=60418473.1/1367-2630/11/1/013014