Eur. Phys. J. B (2017) 90: 66
https://doi.org/10.1140/epjb/e2017-70722-7

Regular Article

Quantum subdiffusion with two- and three-body interactions

¹ Department of Applied Mathematics, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia
² Theory of Control and Dynamical Systems Department, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia
³ Department of Mathematical Software and Supercomputing Technologies, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia
⁴ Center for Theoretical Physics of Complex Systems, Institute for Basic Science, Daejeon 305-732, Korea

^a e-mail: ivanchenko.mv@gmail.com

Received: 7 December 2016
Received in final form: 12 February 2017
Published online: 10 April 2017

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 ~ t^α, 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.