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arXiv · 1612.02470

Quantum subdiffusion with two- and three-body interactions

I. I. Yusipov·T. V. Laptyeva·A. Yu. Pirova·I. B. Meyerov·S. Flach·M. V. Ivanchenko
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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 $\xi_1$ of noninteracting particles. We launch compact wave packets and show that few-body interactions lead to transient subdiffusion of wave packets, $m_2 \sim t^{\alpha}$, $\alpha<1$, on length scales beyond $\xi_1$. The subdiffusion exponent is independent of the number of particles. Two-body interactions yield $\alpha\approx0.5$ for two and three particles, while three-body interactions decrease it to $\alpha\approx0.2$. 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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I. I. Yusipov, T. V. Laptyeva, A. Yu. Pirova, I. B. Meyerov, S. Flach, M. V. Ivanchenko. 2016-12-07. Quantum subdiffusion with two- and three-body interactions. https://doi.org/10.1140/epjb/e2017-70722-7

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