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Quantum subdiffusion with two- and three-body interactions

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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 ξ 1 of noninteracting particles. We launch compact wave packets and show that few-body interactions lead to transient subdiffusion of wave packets, m 2 ~ t α, α< 1, on length scales beyond ξ 1. 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.

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Authors and Affiliations

  1. Department of Applied Mathematics, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia

    Igor I. Yusipov & Mikhail V. Ivanchenko

  2. Theory of Control and Dynamical Systems Department, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia

    Tetyana V. Laptyeva

  3. Department of Mathematical Software and Supercomputing Technologies, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia

    Anna Yu. Pirova & Iosif B. Meyerov

  4. Center for Theoretical Physics of Complex Systems, Institute for Basic Science, Daejeon, 305-732, Korea

    Sergej Flach

Authors
  1. Igor I. Yusipov
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  2. Tetyana V. Laptyeva
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  3. Anna Yu. Pirova
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  4. Iosif B. Meyerov
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  5. Sergej Flach
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  6. Mikhail V. Ivanchenko
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Correspondence to Mikhail V. Ivanchenko.

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Yusipov, I.I., Laptyeva, T.V., Pirova, A.Y. et al. Quantum subdiffusion with two- and three-body interactions. Eur. Phys. J. B 90, 66 (2017). https://doi.org/10.1140/epjb/e2017-70722-7

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  • DOI: https://doi.org/10.1140/epjb/e2017-70722-7

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