Comments on: 285. Dephasing and diffusion of quantum particles

By: NEQNET: The world of theoretical physics ? Blog Archive ? Localization, random matrices, and strong disorder renormalization

Sat, 19 Mar 2011 01:22:43 +0000

[...] Last time I talked about the fate of Anderson localization when the disorder fluctuates in time. This time I [...]

By: Ariel Amir

Ariel Amir — Thu, 26 Feb 2009 11:22:41 +0000

Thanks a lot for correcting the blog. Regarding the -2A_j: if you look at the time derivative of A_{j+1}, for example, it would contain a term T A_j (since the Hamiltonian is hermitian). It is easy to check that the sum of probabilities \sum_j |A_j|^2 is conserved, a direct consequence of the hermiticity of the Hamiltonian. So you don’t need this term. Notice, though, that in the emerging diffusion master equation the term you mentioned exists, to account for the same conservation law in the ‘classical’ case, of diffusion.

Ariel.

By: Dmitry

Dmitry — Thu, 26 Feb 2009 09:51:49 +0000

Dear Ariel,

done! I have a question regarding Laplace operator in (2) and (3) – if this is latticized second order derivative, where is term?

Cheers,
Dmitry.

By: Ariel Amir

Ariel Amir — Thu, 26 Feb 2009 09:46:41 +0000

Yes, sorry for this typo.
What I meant in eq (5) is on the LHS and on the RHS (as you point out to). Eq (6) implies D proportional to (maybe better to omit the equation in this case). Maybe you should change this in the post, to avoid further confusion?

Thanks,

Ariel

By: Dmitry

Dmitry — Wed, 25 Feb 2009 14:29:16 +0000

Hi Ariel,

thanks for explaining dephasing! (or better say – decoherence?) Are ‘s in the formulae (5) and (6) different? I understood that in the r.h.s. is correlation time for the noise, while in the l.h.s. is correlation time for the quantum phase, is it correct?

Cheers,
Dmitry.