Propagating edge states for a magnetic Hamiltonian
| dc.creator | De Bievre, S. | |
| dc.creator | Pule, J. V. | |
| dc.date | 1999-03-16 | |
| dc.date.accessioned | 2026-07-07T04:32:45Z | |
| dc.date.available | 2026-07-07T04:32:45Z | |
| dc.description | We study the quantum mechanical motion of a charged particle moving in a half plane (x>0) subject to a uniform constant magnetic field B directed along the z-axis and to an arbitrary impurity potential W_B, assumed to be weak in the sense that ||W_B||_\infty < δB, for some δsmall enough. We show rigorously a phenomenon pointed out by Halperin in his work on the quantum Hall effect, namely the existence of current carrying and extended edge states in such a situation. More precisely, we show that there exist states propagating with a speed of size B^{1/2} in the y-direction, no matter how fast W_B fluctuates. As a result of this, we obtain that the spectrum of the Hamiltonian is purely absolutely continuous in a spectral interval of size γB (for some γ<1) between the Landau levels of the unperturbed system (i.e. the system without edge or potential), so that the corresponding eigenstates are extended. | |
| dc.description | 14 pages, 1 Figure | |
| dc.identifier | https://arxiv.org/abs/math-ph/9903034 | |
| dc.identifier | http://arxiv.org/abs/math-ph/9903034 | |
| dc.identifier | Mathematical Physics Electronic Journal, vol. 5, 1999 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/58309 | |
| dc.subject | Mathematical Physics | |
| dc.title | Propagating edge states for a magnetic Hamiltonian | |
| dc.type | text |