Landau levels on a torus

Details Landau levels on a torus Landau levels on a torus

2000-07-18

arxiv.org/abs/quant-ph/0007055v1

Int.J.Theor.Phys. 40 (2001) 537-549

Physics

Quantum Physics

10 pages, two color eps-files

Scientific paper

Landau levels have represented a very rich field of research, which has gained widespread attention after their application to quantum Hall effect. In a particular gauge, the holomorphic gauge, they give a physical implementation of Bargmann's Hilbert space of entire functions. They have also been recognized as a natural bridge between Feynman's path integral and Geometric Quantization. We discuss here some mathematical subtleties involved in the formulation of the problem when one tries to study quantum mechanics on a finite strip of sides L_1, L_2 with a uniform magnetic field and periodic boundary conditions. There is an apparent paradox here: infinitesimal translations should be associated to canonical operators [p_x,p_y] \propto i\hslash B, and, at the same time, live in a Landau level of finite dimension B L_1L_2/(hc/e), which is impossible from Wintner's theorem. The paper shows the way out of this conundrum.

Affiliated with

Also associated with

No associations

Rating

Landau levels on a torus does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Landau levels on a torus, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Landau levels on a torus will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-685366