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Teoreticheskaya i Matematicheskaya Fizika, 2010, Volume 162, Number 2, Pages 254–265
DOI: https://doi.org/10.4213/tmf6468
(Mi tmf6468)
 

This article is cited in 24 scientific papers (total in 25 papers)

Rotation number quantization effect

V. M. Buchstaberab, O. V. Karpovb, S. I. Tertychnyib

a Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia
b National Research Institute for Physicotechnical and Radio Engineering Measurements, Moscow, Russia
References:
Abstract: We study a class of dynamical systems on a torus that includes dynamical systems modeling the dynamics of the Josephson transition. For systems in this class, we introduce certain characteristics including a sequence of functions depending on the system parameters. We prove that if this sequence converges at a given point in the parameter space, then its limit is equal to the classical rotation number, and we then call this point a quantization point for the rotation number. We prove that the rotation number of such a system takes only integer values at a quantization point. Quantization areas are thus defined in the parameter space, and the problem of effectively describing them becomes an important part of characterizing the systems under study. We present graphs of the rotation number at quantization points and under conditions when it is not quantized (an example of a half-integer rotation number) and diagrams for quantization areas.
Keywords: dynamical system on a torus, rotation number, quantization, Josephson effect.
Received: 07.09.2009
English version:
Theoretical and Mathematical Physics, 2010, Volume 162, Issue 2, Pages 211–221
DOI: https://doi.org/10.1007/s11232-010-0016-4
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. M. Buchstaber, O. V. Karpov, S. I. Tertychnyi, “Rotation number quantization effect”, TMF, 162:2 (2010), 254–265; Theoret. and Math. Phys., 162:2 (2010), 211–221
Citation in format AMSBIB
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\paper Rotation number quantization effect
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  • https://www.mathnet.ru/eng/tmf/v162/i2/p254
  • This publication is cited in the following 25 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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