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Critical Properties of a Quantum Hierarchical Model

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Abstract

A model of hierarchically interacting quantum anharmonic oscillators is considered. For this model, the sequence of ‘abnormally normed’ fluctuations of the coordinate operator is shown to converge to a nontrivial thermodynamic limit when the model parameters satisfy certain conditions. This is a manifestation of the presence of a critical point for the model. Conditions on the parameters are also found which are sufficient to exclude critical points.

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Authors and Affiliations

  1. Fakultät für Mathematik, Ruhr-Universität, D 44780, Bochum, Germany:

    S. Albeverio

  2. BiBoS Research Centre, Bielefeld, Germany;

    S. Albeverio

  3. Germany

    S. Albeverio

  4. CERFIM, Locarno, Switzerland

    S. Albeverio

  5. BiBosS Research Center, Germany, D 33515 Bielefeld

    YU. G. Kondratiev

  6. Institute of Mathematics, Kiev, Ukraine

    YU. G. Kondratiev

  7. Lviv Academuy of Commerce, Lviv, Ukraine

    YU. V. Kozitsky

Authors
  1. S. Albeverio
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  2. YU. G. Kondratiev
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  3. YU. V. Kozitsky
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Albeverio, S., Kondratiev, Y.G. & Kozitsky, Y.V. Critical Properties of a Quantum Hierarchical Model. Letters in Mathematical Physics 40, 287–291 (1997). https://doi.org/10.1023/A:1007347116692

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  • DOI: https://doi.org/10.1023/A:1007347116692

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