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An exact effective Hamiltonian for a perturbed Landau level

Wilkinson, Michael (1987) An exact effective Hamiltonian for a perturbed Landau level. Journal of Physics A: Mathematical and General, 20 (7). pp. 1761-1771. ISSN 0305-4470. doi:10.1088/0305-4470/20/7/022.

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Considers the effect of a scalar potential V (x, y) on a Landau level in two dimensions. An exact effective Hamiltonian is derived which describes the effect of the potential on a single Landau level, expressed as a power series in V/Ec, where Ec is the cyclotron energy. The effective Hamiltonian can be represented as a function H (x, p) in a one-dimensional phase space. The function H (x, p) resembles the potential V (x, y): when the area of a flux quantum is much smaller than the square of the characteristic length scale of V, then H approximately=V. Also H (x, p) retains the translational and rotational symmetries of V(x, y) exactly, but reflection symmetries are not retained beyond the lowest order of the perturbation expansion.

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Additional Information:Copyright © 1987 Institute of Physics. Received 17 July 1986. Print publication: Issue 7 (11 May 1987) I acknowledge financial support from a Weingart Fellowship of the California Institute of Technology. This work was not supported by any military agency.
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Weingart FoundationUNSPECIFIED
Issue or Number:7
Record Number:CaltechAUTHORS:WILjpa87b
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:11926
Deposited By: Archive Administrator
Deposited On:09 Oct 2008 23:46
Last Modified:12 Jul 2022 19:49

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