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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. doi:10.1103/PhysRevLett.44.1706.

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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
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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.
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NSF Graduate Research FellowshipUNSPECIFIED
Issue or Number:25
Classification Code:PACS numbers: 71.55.Jv, 71.30.+h
Record Number:CaltechAUTHORS:20180417-104512905
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:85893
Deposited By: George Porter
Deposited On:17 Apr 2018 19:42
Last Modified:15 Nov 2021 20:33

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