Bosonic transport through a chain of quantum dots

  • Anton Ivanov
  • Georgios Kordas
  • Andreas Komnik
  • Sandro Wimberger
Regular Article

Abstract

The particle transport through a chain of quantum dots coupled to two bosonic reservoirs is studied. For the case of reservoirs of non-interacting bosonic particles, we derive an exact set of stochastic differential equations, whose memory kernels and driving noise are characterised entirely by the properties of the reservoirs. Going to the Markovian limit an analytically solvable case is presented. The effect of interparticle interactions on the transient behaviour of the system, when both reservoirs are instantaneously coupled to an empty chain of quantum dots, is approximated by a semiclassical method, known as the Truncated Wigner approximation. The steady-state particle flow through the chain and the mean particle occupations are explained via the spectral properties of the interacting system.

Keywords

Mesoscopic and Nanoscale Systems 

References

  1. 1.
    D.P.E. Smith, Science 269, 371 (1995)ADSCrossRefGoogle Scholar
  2. 2.
    K. Terabe, T. Hasegawa, T. Nakayama, M. Aono, Nature 433, 47 (2005)ADSCrossRefGoogle Scholar
  3. 3.
    F.-Q. Xie, L. Nittler, Ch. Obermair, Th. Schimmel, Phys. Rev. Lett. 93, 128303 (2004)ADSCrossRefGoogle Scholar
  4. 4.
    M. Fuechsle, J.A. Miwa, S. Mahapatra, H. Ryu, S. Lee, O. Warschkolow, L.C.L. Hollenberg, G. Klimeck, M.Y. Simmons, Nat. Nanotechnol. 7, 242 (2012)ADSCrossRefGoogle Scholar
  5. 5.
    D.B. Gutman, Y. Gefen, A.D. Mirlin, Phys. Rev. B 85, 125102 (2012)ADSCrossRefGoogle Scholar
  6. 6.
    P. Schlagheck, F. Malet, J.C. Cremon, S.M. Reimann, New J. Phys. 12, 065020 (2010)ADSCrossRefGoogle Scholar
  7. 7.
    L.H. Kristinsdóttir et al., Phys. Rev. Lett. 110, 085303 (2013)ADSCrossRefGoogle Scholar
  8. 8.
    C. Chien, M. Zwolak, M. Ventra, Phys. Rev. A 85, 041601 (2012)ADSCrossRefGoogle Scholar
  9. 9.
    M. Bruderer, W. Belzig, Phys. Rev. A 85, 013623 (2012)ADSCrossRefGoogle Scholar
  10. 10.
    C. Chien, M. Zwolak, M. Ventra, Phys. Rev. A 87, 023609 (2013)ADSCrossRefGoogle Scholar
  11. 11.
    J.H. Thywissen, R.M. Westervelt, M. Prentiss, Phys. Rev. Lett. 83, 3762 (1999)ADSCrossRefGoogle Scholar
  12. 12.
    J. Brantut, J. Meineke, D. Stadler, S. Krinner, T. Esslinger, Science 31, 1069 (2012)ADSCrossRefGoogle Scholar
  13. 13.
    M. Schlosser, J. Kruse, C. Gierl, S. Teichmann, S. Tichelmann, G. Birkl, New J. Phys. 14, 123034 (2012)ADSCrossRefGoogle Scholar
  14. 14.
    J.P. Ronzheimer, M. Schreiber, S. Braun, S.S. Hodgman, S. Langer, I.P. McCulloch, F. Heidrich-Meisner, I. Bloch, U. Schneider, Phys. Rev. Lett. 110, 205301 (2013)ADSCrossRefGoogle Scholar
  15. 15.
    S.C. Caliga, C.J.E. Straatsma, A.A. Zozulya, D.Z. Anderson, arXiv 1208.3109 (2012)Google Scholar
  16. 16.
    R.A. Pepino, J. Cooper, D. Meiser, D.Z. Anderson, M.J. Holland, Phys. Rev. A 82, 013640 (2010)ADSCrossRefGoogle Scholar
  17. 17.
    M. Gajdacz, T. Opatrný, K. Das, arXiv:1207.3108 (2012)Google Scholar
  18. 18.
    A. Polkovnikov, Phys. Rev. A 68, 053604 (2003)ADSCrossRefGoogle Scholar
  19. 19.
    A. Kamenev, Field Theory of Non-Equilibrium Systems (Cambridge University Press, Cambridge, 2007)Google Scholar
  20. 20.
    G. Kordas, S. Wimberger, D. Witthaut, Phys. Rev. A 87, 043618 (2013), Appendix BADSCrossRefGoogle Scholar
  21. 21.
    A. Sinatra, C. Lobo, Y. Castin, J. Phys. B 35, 3599 (2002)ADSCrossRefGoogle Scholar
  22. 22.
    P.B. Blakie, A.S. Bradley, M.J. Davies, R.J. Ballagh, C.W. Gardiner, Adv. Phys. 57, 363 (2008)ADSCrossRefGoogle Scholar
  23. 23.
    J. Rammer,Quantum Field Theory of Non-equilibrium States (Cambridge University Press, Cambridge, 2007)Google Scholar
  24. 24.
    G.D. Mahan, Many particle physics (Kluwer Academic press, New York, 2000)Google Scholar
  25. 25.
    P.W. Anderson, Phys. Rev. 124, 41 (1961)MathSciNetADSCrossRefGoogle Scholar
  26. 26.
    A.J. Leggett, Rev. Mod. Phys. 73, 307 (2001)ADSCrossRefGoogle Scholar
  27. 27.
    D.C. Langreth, Phys. Rev. B 43, 2541 (1991)ADSCrossRefGoogle Scholar
  28. 28.
    T.L. Schmidt, P. Werner, L. Mühlbacher, A. Komnik, Phys. Rev. B 78, 235110 (2008)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Anton Ivanov
    • 1
  • Georgios Kordas
    • 1
  • Andreas Komnik
    • 1
  • Sandro Wimberger
    • 1
  1. 1.Institut für Theoretische PhysikUniversität HeidelbergHeidelbergGermany

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