Quantum subdiffusion with two- and three-body interactions

  • Igor I. Yusipov
  • Tetyana V. Laptyeva
  • Anna Yu. Pirova
  • Iosif B. Meyerov
  • Sergej Flach
  • Mikhail V. Ivanchenko
Regular Article

Abstract

We study the dynamics of a few-quantum-particle cloud in the presence of two- and three-body interactions in weakly disordered one-dimensional lattices. The interaction is dramatically enhancing the Anderson localization length ξ1 of noninteracting particles. We launch compact wave packets and show that few-body interactions lead to transient subdiffusion of wave packets, m2 ~ tα, α< 1, on length scales beyond ξ1. The subdiffusion exponent is independent of the number of particles. Two-body interactions yield α ≈ 0.5 for two and three particles, while three-body interactions decrease it to α ≈ 0.2. The tails of expanding wave packets exhibit exponential localization with a slowly decreasing exponent. We relate our results to subdiffusion in nonlinear random lattices, and to results on restricted diffusion in high-dimensional spaces like e.g. on comb lattices.

Keywords

Solid State and Materials 

References

  1. 1.
    P.W. Anderson, Phys. Rev. 109, 1492 (1958)ADSCrossRefGoogle Scholar
  2. 2.
    S. Aubry, G. Andre, Proc. Israel Phys. Soc. 3, 133 (1980)Google Scholar
  3. 3.
    B. Kramer, A. MacKinnon, Rep. Prog. Phys. 56, 1469 (1993)ADSCrossRefGoogle Scholar
  4. 4.
    F. Evers, A.D. Mirlin, Rev. Mod. Phys. 80, 1355 (2008)ADSCrossRefGoogle Scholar
  5. 5.
    T. Schwartz et al., Nature 446, 52 (2007)ADSCrossRefGoogle Scholar
  6. 6.
    Y. Lahini et al., Phys. Rev. Lett. 100, 013906 (2008)ADSCrossRefGoogle Scholar
  7. 7.
    H. Hu et al., Nat. Phys. 4, 945 (2008)CrossRefGoogle Scholar
  8. 8.
    J. Billy et al., Nature 453, 891 (2008)ADSCrossRefGoogle Scholar
  9. 9.
    G. Roati et al., Nature 453, 895 (2008)ADSCrossRefGoogle Scholar
  10. 10.
    T.V. Laptyeva, M.V. Ivanchenko, S. Flach, J. Phys. A 47, 493001 (2014)CrossRefGoogle Scholar
  11. 11.
    D.M. Basko, I.L. Aleiner, B.L. Altshuler, Ann. Phys. 321, 1126 (2006)ADSCrossRefGoogle Scholar
  12. 12.
    I.L. Aleiner, B.L. Altshuler, G.V. Shlyapnikov, Nat. Phys. 6, 900 (2010)CrossRefGoogle Scholar
  13. 13.
    V.P. Michal, B.L. Altshuler, G.V. Shlyapnikov, Phys. Rev. Lett. 113, 045304 (2014)ADSCrossRefGoogle Scholar
  14. 14.
    O.N. Dorokhov, Sov. Phys. JETP 71, 360 (1990)Google Scholar
  15. 15.
    D.L. Shepelyansky, Phys. Rev. Lett. 73, 2607 (1994)ADSCrossRefGoogle Scholar
  16. 16.
    Y. Imry, Europhys. Lett. 30, 405 (1995)ADSCrossRefGoogle Scholar
  17. 17.
    R.A. Roemer, M. Schreiber, Phys. Rev. Lett. 78, 515 (1997)ADSCrossRefGoogle Scholar
  18. 18.
    K. Frahm, A. Müller-Groeling, J.L. Pichard, D. Weinmann, Europhys. Lett. 31, 169 (1995)ADSCrossRefGoogle Scholar
  19. 19.
    K.M. Frahm, Eur. Phys. J. B 10, 371 (1999)ADSCrossRefGoogle Scholar
  20. 20.
    S. De Toro Arias, X. Waintal, J.-L. Pichard, Eur. Phys. J. B 10, 149 (1999)ADSCrossRefGoogle Scholar
  21. 21.
    D.O. Krimer, R. Khomeriki, S. Flach, JETP Lett. 94, 406 (2011)ADSCrossRefGoogle Scholar
  22. 22.
    K.M. Frahm, Eur. Phys. J. B 89, 115 (2016)ADSCrossRefGoogle Scholar
  23. 23.
    D.L. Shepelyansky, Phys. Rev. B 54, 14896 (1996)ADSCrossRefGoogle Scholar
  24. 24.
    A. Eilmes, U. Grimm, R.A. Römer, M. Schreiber, Eur. Phys. J. B 8, 547 (1999)ADSCrossRefGoogle Scholar
  25. 25.
    S.N. Evangelou, D.E. Katsanos, Phys. Rev. B 56, 12797 (1997)ADSCrossRefGoogle Scholar
  26. 26.
    S. Flach, M. Ivanchenko, R. Khomeriki, Europhys. Lett. 98, 66002 (2012)ADSCrossRefGoogle Scholar
  27. 27.
    K.M. Frahm, D.L. Shepelyansky, Eur. Phys. J. B 88, 337 (2015)ADSCrossRefGoogle Scholar
  28. 28.
    M.V. Ivanchenko, T.V. Laptyeva, S. Flach, Phys. Rev. B 89, 060301 (2014)ADSCrossRefGoogle Scholar
  29. 29.
    D.O. Krimer, S. Flach, Phys. Rev. B 91, 100201 (2015)ADSCrossRefGoogle Scholar
  30. 30.
    F. Dalfovo, S. Giorgini, L. Pitaevskii, S. Stringari, Rev. Mod. Phys. 71, 463 (1999)ADSCrossRefGoogle Scholar
  31. 31.
    I. Bloch, J. Dalibard, W. Zwerger, Rev. Mod. Phys. 80, 885 (2008)ADSCrossRefGoogle Scholar
  32. 32.
    M.I. Molina, Phys. Rev. B 58, 12547 (1998)ADSCrossRefGoogle Scholar
  33. 33.
    A.S. Pikovsky, D.L. Shepelyansky, Phys. Rev. Lett. 100, 094101 (2008)ADSCrossRefGoogle Scholar
  34. 34.
    S. Flach, D.O. Krimer, Ch. Skokos, Phys. Rev. Lett. 102, 024101 (2009)ADSCrossRefGoogle Scholar
  35. 35.
    T.V. Laptyeva, J.D. Bodyfelt, D.O. Krimer, Ch. Skokos, S. Flach, EPL 91, 30001 (2010)ADSCrossRefGoogle Scholar
  36. 36.
    J.D. Bodyfelt, T.V. Laptyeva, G. Gligoric, D.O. Krimer, Ch. Skokos, S. Flach, Phys. Rev. E 84, 016205 (2011)ADSCrossRefGoogle Scholar
  37. 37.
    A. Pikovsky, S. Fishman, Phys. Rev. E 83, 025201 (2011)ADSCrossRefGoogle Scholar
  38. 38.
    M. Larcher, T.V. Laptyeva, J.D. Bodyfelt, F. Dalfovo, M. Modugno, S. Flach, New J. Phys. 14, 103036 (2012)ADSCrossRefGoogle Scholar
  39. 39.
    Ch. Skokos, I. Gkolias, S. Flach, Phys. Rev. Lett. 111, 064101 (2013)ADSCrossRefGoogle Scholar
  40. 40.
    T.V. Laptyeva, J.D. Bodyfelt, S. Flach, Physica D 256, 1 (2013)ADSMathSciNetCrossRefGoogle Scholar
  41. 41.
    M. Mulansky, A. Pikovsky, New J. Phys. 15, 053015 (2013)ADSMathSciNetCrossRefGoogle Scholar
  42. 42.
    D.M. Basko, Phys. Rev. E 89, 022921 (2014)ADSCrossRefGoogle Scholar
  43. 43.
    Ch. Skokos, S. Flach, Phys. Rev. E 82, 016208 (2010)ADSCrossRefGoogle Scholar
  44. 44.
    M. Mulansky, A. Pikovsky, New J. Phys. 15, 053015 (2013)ADSMathSciNetCrossRefGoogle Scholar
  45. 45.
    H.P. Büchler, A. Micheli, P. Zoller, Nat. Phys. 3, 726 (2007)CrossRefGoogle Scholar
  46. 46.
    X. Waintal, J.-L. Pichard, Eur. Phys. J. B 6, 117 (1998)ADSCrossRefGoogle Scholar
  47. 47.
    G.H. Weiss, S. Halvin, Physica A 134, 474 (1986)ADSCrossRefGoogle Scholar
  48. 48.
    V.E. Arkhincheev, Chaos 17, 043102 (2007)ADSMathSciNetCrossRefGoogle Scholar
  49. 49.
    P. Illien, O. Bénichou, J. Phys. A 49, 265001 (2016)ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Igor I. Yusipov
    • 1
  • Tetyana V. Laptyeva
    • 2
  • Anna Yu. Pirova
    • 3
  • Iosif B. Meyerov
    • 3
  • Sergej Flach
    • 4
  • Mikhail V. Ivanchenko
    • 1
  1. 1.Department of Applied MathematicsLobachevsky State University of Nizhny NovgorodNizhny NovgorodRussia
  2. 2.Theory of Control and Dynamical Systems Department, Lobachevsky State University of Nizhny NovgorodNizhny NovgorodRussia
  3. 3.Department of Mathematical Software and Supercomputing TechnologiesLobachevsky State University of Nizhny NovgorodNizhny NovgorodRussia
  4. 4.Center for Theoretical Physics of Complex Systems, Institute for Basic ScienceDaejeonKorea

Personalised recommendations