Skip to main content
SpringerLink
Log in

Statistical Properties of Disordered Quantum Systems

  • Conference paper
Recent Advances in Operator Theory, Operator Algebras, and their Applications

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 153))

Abstract

We discuss two different approaches to the study of the long-time behavior of some disordered quantum anharmonic chains.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. H. Araki, On Quasi-Free States of the Canonical Commutation Relations. II, Publ. Res. Inst. Math. Sci. 7 (1971–72), 121–152.

    Google Scholar 

  2. H. Araki, M. Shiraishi, On Quasi-Free States of the Canonical Commutation Relations. I, Publ. Res. Inst. Math. Sci. 7 (1971–72), 105–120.

    Google Scholar 

  3. O. Bratteli, D.W. Robinson, Operator Algebras and Quantum Statistical Mechanics. I, II, Springer, Berlin-Heidelberg-New York, 1981.

    Google Scholar 

  4. P. de Smedt, D. Dürr, J.L. Lebowitz, C. Liverani, Quantum System in Contact with a Thermal Environment: Rigorous Treatment of a Simple Model. Commun. Math. Phys. 120 (1988), 195–231.

    Google Scholar 

  5. D. Dürr, V. Naroditsky, N. Zanghi, On the Hydrodynamic Motion of a Test Particle in a Random Chain. Ann. Phys. 178 (1987), 74–88.

    Google Scholar 

  6. F. Fidaleo, C. Liverani, Ergodic Properties for a Quantum Nonlinear Dynamics. J. Stat. Phys. 97 (1999), 957–1009.

    Google Scholar 

  7. F. Fidaleo, C. Liverani, Ergodic Properties of a Model Related to Disordered Quantum Anharmonic Crystals. Commun. Math. Phys. 235 (2003), 169–189.

    Google Scholar 

  8. V. Jakši’c, C.-A. Pillet, Mathematical Theory Of Non-Equilibrium Quantum Statistical Mechanics. J. Stat. Phys. 108 (2002), 787–829.

    Google Scholar 

  9. D. Kastler, Equilibrium States of Matter and Operator Algebras. In Symposia Mathematica Vol. XX (1976), 49–107, Academic Press.

    Google Scholar 

  10. H. Kunz, B. Souillard, Sur le spectre des opérateurs aux différence finies aléatoires. Commun. Math. Phys. 78 (1986), 201–246.

    Google Scholar 

  11. C.P. Niculescu, A. Ströh, L. Zsidó, Noncommutative Extension of Classical and Multiple Recurrence Theorems. J. Operator Theory 50 (2003), 3–52.

    Google Scholar 

  12. M. Spivak, Calculus on Manifolds. Benjamin, New York-Amsterdam, 1965.

    Google Scholar 

  13. G. Szegő, Orthogonal Polynomials. Coll. Math. Vol. 23, American Mathematical Society, Providence, 1981.

    Google Scholar 

  14. M. Takesaki, Theory of Operator Algebras. I, Springer, Berlin-Heidelberg-New York 1979.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Universitá di Tor Vergata, via della Ricerca Scientifica 1, I-00133, Roma, Italy

    Carlangelo Liverani

Authors
  1. Francesco Fidaleo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Carlangelo Liverani
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of the West Timişoara, Bul. V. Parvan Nr. 4, 1900, Timişoara, Romania

    Dumitru Gaşpar

  2. Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, Bucharest, 70700, Romania

    Dan Timotin

  3. Dipartimento di Matematica, Università di Roma „Tor Vergata”, Via della Ricerca Scientifica 1, 00133, Roma, Italy

    László Zsidó

  4. School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, 69978, Israel

    Israel Gohberg

  5. Laboratoire AGAT-UMR 8524 U.F.R. de mathématiques, Université des Sciences et Technologie de Lille, 59655, Villeneuve d’Ascq Cedex, France

    Florian-Horia Vasilescu

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Birkhäuser Verlag Basel/Switzerland

About this paper

Cite this paper

Fidaleo, F., Liverani, C. (2004). Statistical Properties of Disordered Quantum Systems. In: Gaşpar, D., Timotin, D., Zsidó, L., Gohberg, I., Vasilescu, FH. (eds) Recent Advances in Operator Theory, Operator Algebras, and their Applications. Operator Theory: Advances and Applications, vol 153. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7314-8_7

Download citation

Publish with us

Policies and ethics

Search

Navigation