Noise Induced Dissipation in Discrete-Time Classical and Quantum Dynamical Systems

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Wolowski, Lech;
  • Publisher: eScholarship, University of California
  • Subject: Nonlinear Sciences - Chaotic Dynamics | math.DS | Physical Sciences and Mathematics | Mathematics - Dynamical Systems | nlin.CD

We introduce a new characteristics of chaoticity of classical and quantum dynamical systems by defining the notion of the dissipation time which enables us to test how the system responds to the noise and in particular to measure the speed at whi... View more
  • References (42)
    42 references, page 1 of 5

    [10] Arnold V. I. and A. Avez: Ergodic Problems of Classical Mechanics. The Mathematical Physics Monograph Series, W.A. Benjamin, 1968.

    [11] Artin M. and B. Mazur: On periodic points, Ann. Math. 81:1, 82-99 (1965).

    [12] Baladi V.: Positive Transfer Operators and Decay of Correlations. Advanced Series in Nonlinear Dynamics vol. 16 , World Scientific, 2000.

    [13] Baladi V.: Decay of Correlations. Proceedings of Symposia in Pure Mathematics. 69 (2001), 297-325.

    [14] Baladi V. and L.-S. Young: On the Spectra of Randomly Perturbed Expanding Maps. Commun. Math. Phys. 156 (1993), 355-385; Erratum: Commun. Math. Phys. 166 (1994), 219-220.

    [15] Balazs N.L. and A. Voros: The quantized Baker's transformation. Annals of Physics 190, (1989) 1-31.

    [16] Benatti F., V. Cappellini, M. De Cock, M. Fannes and D. Vanpeteghem, Classical Limit of Quantum Dynamical Entropies. Preprint quant-ph/0308069.

    [21] Blank M., G. Keller and C. Liverani: Ruelle-Perron-Frobenius spectrum for Anosov maps. Nonlinearity 15 (2002), 1905-1973.

    [22] Bonechi F. and S. De Bi`evre: Exponential mixing and ln~ timescales in quantized hyperbolic maps on the torus. Commun. Math. Phys. 211 (2000), 659-686.

    [23] Bonechi F. and S. De Bi`evre: Controlling strong scarring for quantized ergodic toral automorphisms. Duke Math. J. 117 (2003), no. 3, 571-587.

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