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Teoreticheskaya i Matematicheskaya Fizika, 2004, Volume 139, Number 3, Pages 477–490
DOI: https://doi.org/10.4213/tmf67
(Mi tmf67)
 

This article is cited in 4 scientific papers (total in 4 papers)

The Relation and Evolution of Squeezing and Instability for Systems with Quadratic Hamiltonians

V. I. Kuvshinova, V. V. Marmyshb, V. A. Shaporova

a B. I. Stepanov Institute of Physics, National Academy of Sciences of Belarus
b Belarusian State University
Full-text PDF (385 kB) Citations (4)
References:
Abstract: We propose a method that allows relating the quantum squeezing effect to the classical instability by establishing evolution equations for elements of the dispersion matrix directly in terms of elements of the stability matrix. The solution of these equations is written in terms of the evolution operator. Knowing this operator, we can analyze the system instability at finite times. Based on the developed formalism, we investigate two physical systems: the degenerate and nondegenerate parametric amplifiers with external $\delta$-shaped pulses. We show that we can either amplify or, on the contrary, weaken both the squeezing effect and the system instability using $\delta$-pulses.
Keywords: squeezing, instability, stability matrix, dispersion matrix, evolution operator, Lyapunov exponent.
Received: 03.06.2003
English version:
Theoretical and Mathematical Physics, 2004, Volume 139, Issue 3, Pages 846–858
DOI: https://doi.org/10.1023/B:TAMP.0000029706.01419.bb
Bibliographic databases:
Language: Russian
Citation: V. I. Kuvshinov, V. V. Marmysh, V. A. Shaporov, “The Relation and Evolution of Squeezing and Instability for Systems with Quadratic Hamiltonians”, TMF, 139:3 (2004), 477–490; Theoret. and Math. Phys., 139:3 (2004), 846–858
Citation in format AMSBIB
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\paper The Relation and Evolution of Squeezing and Instability for Systems with Quadratic Hamiltonians
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\pages 477--490
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\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2004TMP...139..846K}
\elib{https://elibrary.ru/item.asp?id=13914731}
\transl
\jour Theoret. and Math. Phys.
\yr 2004
\vol 139
\issue 3
\pages 846--858
\crossref{https://doi.org/10.1023/B:TAMP.0000029706.01419.bb}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000222713300009}
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  • https://www.mathnet.ru/eng/tmf67
  • https://doi.org/10.4213/tmf67
  • https://www.mathnet.ru/eng/tmf/v139/i3/p477
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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    Abstract page:662
    Full-text PDF :212
    References:85
    First page:1
     
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