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On Invariant Subspace In Quantum Control Systems and Some Concepts of Integrable Quantum Systems

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Abstract

Trajectories of some dynamical systems can be analysed by algebraic methods. In this paper we discuss certain applications of the so-called Shemesh criterion and its generalisations to analysis of properties of quantum control systems. In particular, some Hamiltonians with non-degenerated spectrum are considered, and also the case of a Hamiltonian with m 1,...,m N degeneracies, where \({\sum }^{N}_{i=1}m_{i}=n\), is discussed.

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Acknowledgments

This research has been supported by grant No. DEC-2011/02/A/ST1/00208 of National Science Center of Poland.

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Authors and Affiliations

  1. Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Toruń, Poland

    Andrzej Jamiołkowski & Takeo Kamizawa

  2. Center for Theoretical Physics of the Polish Academy of Sciences, Warsaw, Poland

    Grzegorz Pastuszak

Authors
  1. Andrzej Jamiołkowski
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  2. Takeo Kamizawa
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  3. Grzegorz Pastuszak
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Corresponding author

Correspondence to Takeo Kamizawa.

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Jamiołkowski, A., Kamizawa, T. & Pastuszak, G. On Invariant Subspace In Quantum Control Systems and Some Concepts of Integrable Quantum Systems. Int J Theor Phys 54, 2662–2674 (2015). https://doi.org/10.1007/s10773-014-2498-6

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  • DOI: https://doi.org/10.1007/s10773-014-2498-6

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