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Asymptotic nonequilibrium steady-state operators

M. F. Gelin

D. S. Kosov

  • Department of Chemistry, Technical University of Munich, Lichtenbergstrasse 4, D-85747 Garching, Germany

  • Department of Physics and Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Campus Plaine, CP 231, Boulevard du Triomphe, B-1050 Brussels, Belgium and Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742, USA

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Phys. Rev. E 80, 022101 – Published 11 August, 2009

DOI: https://doi.org/10.1103/PhysRevE.80.022101

Abstract

We present a method for the calculation of asymptotic operators for nonequilibrium steady-state quantum systems. The asymptotic steady-state operator is obtained by averaging the corresponding operator in Heisenberg representation over infinitely long time. Several examples are considered to demonstrate the utility of our method. The results obtained within our approach are compared to those obtained within the Schwinger-Keldysh nonequilibrium Green’s functions.

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References (41)

  1. P. Gaspard, Prog. Theor. Phys. Suppl. 165, 33 (2006).
  2. N. Agrait, A. L. Yeyati, and J. M. van Ruitenbeek, Phys. Rep. 377, 81 (2003).
  3. D. Andrieux and P. Gaspard, Phys. Rev. E 74, 011906 (2006).
  4. A. B. Kolomeisky and M. E. Fisher, Annu. Rev. Phys. Chem. 58, 675 (2007).
  5. Y. Togashi and A. S. Mikhailov, Proc. Natl. Acad. Sci. U.S.A. 104, 8697 (2007).
  6. A. Nitzan and M. A. Ratner, Science 300, 1384 (2003).
  7. A. Dhar, Phys. Rev. Lett. 86, 5882 (2001).
  8. A. Dhar and J. L. Lebowitz, Phys. Rev. Lett. 100, 134301 (2008).
  9. D. Segal, Phys. Rev. Lett. 100, 105901 (2008).
  10. D. G. Cahill, W. K. Ford, K. E. Goodson, G. D. Mahan, A. Majumdar, H. J. Maris, R. Merlin, and S. R. Phillpot, J. Appl. Phys. 93, 793 (2003).
  11. L. Venkataraman, J. Klare, I. Tam, C. Nuckolls, M. Hybertsen, and M. Steigerwald, Nano Lett. 6, 458 (2006).
  12. B. Xu and N. J. Tao, Science 301, 1221 (2003).
  13. L. V. Keldysh, Zh. Eksp. Teor. Fiz. 47, 1515 (1965) [Sov. Phys. JETP 20, 1018 (1965)].
  14. C. Caroli, R. Combesco, P. Nozieres, and D. Saintjam, J. Phys. C 4, 916 (1971).
  15. A. P. Jauho, N. S. Wingreen, and Y. Meir, Phys. Rev. B 50, 5528 (1994).
  16. Y. Meir and N. S. Wingreen, Phys. Rev. Lett. 68, 2512 (1992).
  17. Y. Dahnovsky, J. Chem. Phys. 127, 014104 (2007).
  18. Y. Dahnovsky, J. Chem. Phys. 126, 234111 (2007).
  19. J. Rammer, Quantum Field Theory of Non-equilibrium States (Cambridge University Press, Cambridge, 2007).
  20. M. Di Ventra, S. T. Pantelides, and N. D. Lang, Phys. Rev. Lett. 84, 979 (2000).
  21. N. D. Lang, Phys. Rev. B 52, 5335 (1995).
  22. D. N. Zubarev, Nonequilibrium Statistical Thermodynamics (Consultants Bureau, New York, 1974).
  23. S. Hershfield, Phys. Rev. Lett. 70, 2134 (1993).
  24. S. Tasaki and J. Takahashi, Prog. Theor. Phys. 165, 57 (2006).
  25. M. F. Gelin and D. S. Kosov, Phys. Rev. E 78, 011116 (2008).
  26. F. B. Anders, Phys. Rev. Lett. 101, 066804 (2008).
  27. E. T. Jaynes, Phys. Rev.106, 620 (1957).
  28. M. D. Johnson and O. Heinonen, Phys. Rev. B 51, 14421 (1995).
  29. D. S. Kosov, J. Chem. Phys. 116, 6368 (2002).
  30. D. S. Kosov, J. Chem. Phys. 120, 7165 (2004).
  31. P. Bokes, H. Mera, and R. W. Godby, Phys. Rev. B 72, 165425 (2005).
  32. D. S. Kosov, J. Chem. Phys. 119, 1 (2003).
  33. D. S. Kosov and J. C. Greer, Phys. Lett. A 291, 46 (2001).
  34. A. Painelli, Phys. Rev. B 74, 155305 (2006).
  35. R. Kubo, Lectures in Theoretical Physics, edited by W. Britten (Interscience, New York, 1959), Vol. 1, p. 120.
  36. W. Grandy, Foundations of Statistical Mechanics: Volume II: Nonequilibrium Phenomena (Fundamental Theories of Physics) (Springer, New York, 1988).
  37. F. R. Gantmacher, Applications of the Theory of Matrices (Dover, New York, 2005).
  38. A. Dhar and D. Sen, Phys. Rev. B 73, 085119 (2006).
  39. M. H. Cohen, L. M. Falicov, and J. C. Phillips, Phys. Rev. Lett. 8, 316 (1962).
  40. A. Arnold, F. Weigend, and F. Evers, J. Chem. Phys. 126, 174101 (2007).
  41. A heat flow through the system can be studied in exactly the same way as a particle current. We simply need to define the energy current operator as JE=ddt∑lεlal†al=i∑lsεlTls(al†as−as†al).

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Phys. Rev. E 80, 022101– Published 11 August, 2009
  • Received 24 March 2009

© 2009 American Physical Society

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