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Quantum and Classical Evolutions of a Nonautonomous Dynamical System—A Comparison

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Abstract

The influence of moving boundaries on the stability of quantum Hamiltonian systems, in particular on the dynamics of quantum versions of the classical Pustilnikov model, is investigated (the latter consists of a masspoint bouncing above an oscillating plate under the influence of constant gravity.) It is shown that, in contrast to the classical Pustilnikov model, generic time-periodic boundary conditions (including the Dirichlet condition) on the quantum models do not allow unlimited energy gain (“speeding up”) of these systems.

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REFERENCES

  1. H. R. Jauslin, Stability and chaos in classical and quantum Hamiltonian systems. Proc. II Granada Seminar on Computational Physics (Singapore, World Scientific, 1993).

    Google Scholar 

  2. L. D. Pustilnikov, Stable and oscillating motions in nonautonomous dynamical systems, Trans. Moscow Math. Soc. 2:1-101 (1978).

    Google Scholar 

  3. G. Karner, The Schrödinger equation on non-stationary domains, Electr. J. Diff. Eqs. 1998, No. 20:1-20 (1998). Available under the address http: //ejde.math.swt.edu/Volumes/ 1998/20-Karner/

    Google Scholar 

  4. H. L. Cycon, R. G. Froese, W. Kirsch, and B. Simon, Schrödinger Operators (New York, Springer, 1987).

    Google Scholar 

  5. G. Karner, The classical limit of Floquet operators with singular spectrum, J. Math. Anal. Appl. 164:206-218 (1992).

    Google Scholar 

  6. J. Weidmann, Linear Operators in Hilbert Spaces (New York, Springer, 1980).

    Google Scholar 

  7. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (New York, Dover Publications, 1972).

    Google Scholar 

  8. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systemts, and Bifurcations of Vector Fields (New York, Springer, 1983).

    Google Scholar 

  9. G. Karner, On quantum twist maps and spectral properties of Floquet Hamiltonians, Ann. Inst. H. Poincaré 68:139-157 (1998).

    Google Scholar 

  10. W. Thirring, Lehrbuch der Mathematischen Physik, Vol. 4 (Wien, Springer, 1979).

    Google Scholar 

  11. F. Benvenuto, G. Casati, I. Guarneri, and D. L. Shepelyansky, A quantum transition from localized to extended states in a classically chaotic system, Z. Phys. B 84:159-163 (1991).

    Google Scholar 

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  1. Institut für Kerntechnik und Reaktorsicherheit, Universität Karlsruhe (TH), D-76021, Karlsruhe, Germany

    Gunther Karner

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  1. Gunther Karner
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Karner, G. Quantum and Classical Evolutions of a Nonautonomous Dynamical System—A Comparison. Journal of Statistical Physics 96, 627–637 (1999). https://doi.org/10.1023/A:1004598223382

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  • DOI: https://doi.org/10.1023/A:1004598223382

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