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TMF, 2002, Volume 133, Number 1, Pages 87–102 (Mi tmf382)  

This article is cited in 1 scientific paper (total in 1 paper)

Spectral Properties of Hamiltonians of Charged Systems in a Homogeneous Magnetic Field: I. General Characteristic of the Spectrum

G. M. Zhislin

Scientific Research Institute of Radio Physics

Abstract: We study the spectrum of Hamiltonians of charged multiparticle systems in a homogeneous magnetic field with a fixed sum $P_{\Sigma }$ of the pseudomomentum components and without it. We prove that if $P_{\Sigma }$ is fixed, then the spectrum of Hamiltonians is independent of the value of $P_{\Sigma }$, while the spectrum without fixation of $P_{\Sigma }$ coincides with the spectrum with fixation and differs from the latter only by some additional infinite degeneration (this is a principal difference between problems with a homogeneous magnetic field and problems without any field in which the absence of any fixation of the total angular momentum results in “covering” the spectrum of the relative motion by a continuous spectrum). We find the continuous spectrum of the Hamiltonians and characterize the spectrum of Hamiltonians of two-cluster mutually noninteracting systems obtained by decomposing the original system in the state with a fixed value of $P_{\Sigma }$. The last result is necessary for the study of the purely point spectrum.

Keywords: Hamiltonian, homogeneous magnetic field, spectral properties, relative motion, pseudomomentum

DOI: https://doi.org/10.4213/tmf382

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English version:
Theoretical and Mathematical Physics, 2002, 133:1, 1390–1405

Bibliographic databases:

Received: 18.01.2002

Citation: G. M. Zhislin, “Spectral Properties of Hamiltonians of Charged Systems in a Homogeneous Magnetic Field: I. General Characteristic of the Spectrum”, TMF, 133:1 (2002), 87–102; Theoret. and Math. Phys., 133:1 (2002), 1390–1405

Citation in format AMSBIB
\Bibitem{Zhi02}
\by G.~M.~Zhislin
\paper Spectral Properties of Hamiltonians of Charged Systems in a~Homogeneous Magnetic Field: I.~General Characteristic of the Spectrum
\jour TMF
\yr 2002
\vol 133
\issue 1
\pages 87--102
\mathnet{http://mi.mathnet.ru/tmf382}
\crossref{https://doi.org/10.4213/tmf382}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1992171}
\zmath{https://zbmath.org/?q=an:1066.81010}
\transl
\jour Theoret. and Math. Phys.
\yr 2002
\vol 133
\issue 1
\pages 1390--1405
\crossref{https://doi.org/10.1023/A:1020698031079}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000179367800006}


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  • https://doi.org/10.4213/tmf382
  • http://mi.mathnet.ru/eng/tmf/v133/i1/p87

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    This publication is cited in the following articles:
    1. G. M. Zhislin, “Spectral Properties of Hamiltonians of Charged Systems in a Homogeneous Magnetic Field: II. The Structure of the Pure Point Spectrum”, Theoret. and Math. Phys., 134:2 (2003), 240–253  mathnet  crossref  crossref  mathscinet  zmath  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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