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

DOI: 10.1140/epjb/e2017-70722-7

Cite this article as:
Yusipov, I.I., Laptyeva, T.V., Pirova, A.Y. et al. Eur. Phys. J. B (2017) 90: 66. doi:10.1140/epjb/e2017-70722-7
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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 

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

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