Skip to main content
SpringerLink
Log in

A model of nonautonomous dynamics driven by repeated harmonic interaction

  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

Abstract

We consider an exactly solvable model of nonautonomous W*-dynamics driven by repeated harmonic interaction. The dynamics is Hamiltonian and quasifree. Because of inelastic interaction in the large-time limit, it leads to relaxation of initial states to steady states. We derive the explicit entropy production rate accompanying this relaxation. We also study the evolution of different subsystems to elucidate their eventual correlations and convergence to equilibriums. In conclusion, we prove that the W*-dynamics manifests a universal stationary behavior in a short-time interaction limit.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. H. Tamura and V. A. Zagrebnov, “A dynamics driven by repeated harmonic perturbations,” arXiv:1404.2998v1 [math.FA] (2014).

  2. B. Nachtergaele, A. Vershynina, and V. A. Zagrebnov, Ann. Henri Poincaré, 15, 213–262 (2014); arXiv: 1206.6169v4 [math-ph] (2012).

    Article  ADS  MathSciNet  Google Scholar 

  3. L. Bruneau, A. Joye, and M. Merkli, J. Math. Phys., 55, 075204 (2014); arXiv:1305.2472v1 [math-ph] (2013).

    Article  ADS  MathSciNet  Google Scholar 

  4. O. Bratteli and D. W. Robinson, Operator Algebras and Quantum Statistical Mechanics 2: Equilibrium States. Models in Quantum Statistical Mechanics, Springer, Berlin (1997).

    Book  MATH  Google Scholar 

  5. V. A. Zagrebnov, Topics in the Theory of Gibbs Semigroups (Leuven Notes Math. Theor. Phys. Ser. A: Math. Phys., Vol. 10), KU Leuven Univ. Press, Leuven (2003).

    MATH  Google Scholar 

  6. S. Attal, A. Joye, and C.-A. Pillet, eds., Open Quantum Systems I: The Hamiltonian Approach (Lect. Notes Math., Vol. 1880), Springer, Berlin (2006).

    MATH  Google Scholar 

  7. A. F. Verbeure, Many-Body Boson Systems: Half a Century Later, Springer, Berlin (2011).

    Book  MATH  Google Scholar 

  8. M. Fannes, Ann. Inst. Henri Poincaré Sect. A, ns., 28, 187–196 (1978).

    MathSciNet  Google Scholar 

  9. H. Araki, Publ. Res. Inst. Math. Sci., 11, 809–833 (1976).

    Article  MathSciNet  Google Scholar 

  10. S. Attal, A. Joye, and C.-A. Pillet, eds., Open Quantum Systems III: Recent Developments (Lect. Notes Math., Vol. 1882), Springer, Berlin (2006).

    MATH  Google Scholar 

  11. S. Attal and Y. Pautrat, Ann. Inst. Henri Poincaré, 7, 59–104 (2006).

    Article  MathSciNet  Google Scholar 

  12. S. Attal, A. Joye, and C.-A. Pillet, eds., Open Quantum Systems II: The Markovian Approach (Lect. Notes Math., Vol. 1881), Springer, Berlin (2006).

    MATH  Google Scholar 

  13. S. Attal and C. Pellegrini, Open Syst. Inf. Dyn., 17, 389–408 (2010).

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut de Mathématiques de Marseille, Marseille, France

    V. A. Zagrebnov

  2. Département de Mathématiques, Université d’Aix-Marseille, Marseille, France

    V. A. Zagrebnov

  3. Institute of Science and Engineering, Graduate School of the Natural Science and Technology, Kanazawa University, Kanazawa, Japan

    H. Tamura

Authors
  1. V. A. Zagrebnov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. Tamura
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. A. Zagrebnov.

Additional information

The research of H. Tamura was supported by the JSPS (Grant-in-Aid for Scientific Research (C) 24540168).

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 187, No. 3, pp. 531–559, June, 2016.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zagrebnov, V.A., Tamura, H. A model of nonautonomous dynamics driven by repeated harmonic interaction. Theor Math Phys 187, 909–934 (2016). https://doi.org/10.1134/S004057791606009X

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S004057791606009X

Keywords

Search

Navigation