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Quantum Magnetic Hamiltonians with Remarkable Spectral Properties

Miller, Keith and Simon, Barry (1980) Quantum Magnetic Hamiltonians with Remarkable Spectral Properties. Physical Review Letters, 44 (25). pp. 1706-1707. ISSN 0031-9007. http://resolver.caltech.edu/CaltechAUTHORS:20180417-104512905

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Abstract

The Hamiltonian, H, of a spinless particle moving in two dimensions in an axially symmetric magnetic field B(ρ) is considered. If B(ρ) ∼ ρ^(−α) for ρ, large with 0 < α < 1, then it is shown that H has spectrum [0, ∞) with only eigenvectors and eigenvalues dense in [0, ∞). If α = 1, then the spectrum is a dense point spectrum in [0, c] for suitable c and absolutely continuous in [c, ∞).


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevLett.44.1706DOIArticle
ORCID:
AuthorORCID
Simon, Barry0000-0003-2561-8539
Additional Information:© 1980 American Physical Society. (Received 3 March 1980) It is a pleasure to thank J. Hopfield and V. Enss for emphasizing to us that we should look at the classical case. This research was supported in part by the National Science Foundation under Grant No. MCS-78-01885.
Funders:
Funding AgencyGrant Number
NSF Graduate Research FellowshipUNSPECIFIED
NSFMCS-78-01885
Classification Code:PACS numbers: 71.55.Jv, 71.30.+h
Record Number:CaltechAUTHORS:20180417-104512905
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20180417-104512905
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:85893
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:17 Apr 2018 19:42
Last Modified:17 Apr 2018 19:42

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