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Dynamic invariants and the berry phase for generalized driven harmonic oscillators

Journal of Russian Laser Research volume 32, pages 486–494 (2011)Cite this article

Abstract

We present quadratic dynamic invariants and evaluate the Berry phase for the time-dependent Schrödinger equation with the most general variable quadratic Hamiltonian.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Western Washington University, Bellingham, WA, 98225-9063, USA

    Barbara Sanborn

  2. School of Mathematical and Statistical Sciences and Mathematical, Computational and Modeling Sciences Center Arizona State University, Tempe, AZ, 85287-1804, USA

    Sergei K. Suslov

  3. Centre de Recherches Mathématiques, Université de Montréal Montréal, Québec, Centre-ville Station, P.O. Box 6128, Canada, H3C 3J7

    Luc Vinet

Authors
  1. Barbara Sanborn
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  2. Sergei K. Suslov
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  3. Luc Vinet
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Correspondence to Sergei K. Suslov.

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Sanborn, B., Suslov, S.K. & Vinet, L. Dynamic invariants and the berry phase for generalized driven harmonic oscillators. J Russ Laser Res 32, 486–494 (2011). https://doi.org/10.1007/s10946-011-9238-7

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Keywords

  • time-dependent Schrödinger equation
  • generalized harmonic oscillators
  • Green function
  • dynamic invariants
  • Berry phase
  • Ermakov-type system