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Coherent Transport and Dynamical Entropy for Fermionic Systems

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This paper consists of two parts. First we set up a general scheme of local traps in a homogeneous deterministic quantum system. The current of particles caught by the trap is linked to the dynamical behaviour of the trap states. In this way, transport properties in a homogeneous system are related to spectral properties of a coherent dynamics. Next we apply the scheme to a system of Fermions in the one-particle approximation. We obtain in particular lower bounds for the dynamical entropy in terms of the current induced by the trap.

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REFERENCES

  1. J. Bellissard, Coherent and dissipative transport in aperiodic solids, in Dynamics of Dissipation, P. Garbaczewski and R Olkiewicz, eds., Lecture Notes in Physics, Vol. 597 (Springer, 2002), pp. 413–486.

  2. D. K. Wójcik and J. R. Dorfman, Quantum multibaker maps I: Extreme quantum regime, Phys. Rev. E 66:036110(2002).

    Google Scholar 

  3. E. Størmer and D. Voiculescu, Entropy of Bogoliubov automorphisms of the Canonical Anticommutation Relations, Commun. Math. Phys. 133:521–542 (1990).

    Google Scholar 

  4. P. Gaspard, Chaos, Scattering, and Statistical Mechanics (Cambridge University Press, Cambridge, 1998).

    Google Scholar 

  5. F. Benatti and H. Narnhofer, Entropic dimension for completely positive maps, J. Stat. Phys. 53:1273(1988).

    Google Scholar 

  6. F. Spitzer, Principles of Random Walk, 2nd ed. (Springer-Verlag, New York, 1976).

    Google Scholar 

  7. P. Gaspard, Dynamical Theory of Relaxation in Classical and Quantum Systems, P. Garbaczewski and R. Olkiewicz, eds., Lecture Notes in Physics, Vol. 597 (Springer, 2002), pp. 111–164.

  8. S. Tasaki, Thermodynamic Behavior of Large Dynamical Systems—Quantum 1d Conductor and Classical Multibaker Map—, P. Garbaczewski and R. Olkiewicz, eds., Lecture Notes in Physics, Vol. 597 (Springer, 2002), pp. 395–412.

  9. D. Armstead, B. R. Hunt, and E. Ott, Long time algebraic relaxation in chaotic billiards, Phys. Rev. Lett. 89:284101(2002).

    Google Scholar 

  10. R. L. Cooke: Analysis seminar 2000–2001, Lecture 0, http://www.emba.uvm.edu/∷cooke/seminar/seminar.html.

  11. L. H. Loomis, A note on the Hilbert transform, Bull. Amer. Soc. 52:1082–1086 (1946).

    Google Scholar 

  12. R. del Rio, S. Jitomirskaya, Y. Last, and B. Simon, Operators with singular continu-ous spectrum, IV. Hausdorff dimensions, rank one perturbations, and localization,J. d'Analyse Math. 69:153–200 (1996).

    Google Scholar 

  13. R. Alicki and M. Fannes, Defining quantum dynamical entropy, Lett. Math. Phys. 32:75–82 (1994).

    Google Scholar 

  14. R. Alicki and M. Fannes, Quantum Dynamical Systems (Oxford University Press, Oxford, 2001).

    Google Scholar 

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Alicki, R., Fannes, M., Haegeman, B. et al. Coherent Transport and Dynamical Entropy for Fermionic Systems. Journal of Statistical Physics 113, 549–574 (2003). https://doi.org/10.1023/A:1026020802400

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  • DOI: https://doi.org/10.1023/A:1026020802400

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