Quantum subdiffusion with two- and three-body interactions

TL;DR

This paper investigates how few-body interactions in disordered one-dimensional lattices cause transient subdiffusion, revealing interaction-dependent exponents and exponential localization tails, with implications for understanding quantum transport.

Contribution

It demonstrates that few-body interactions induce transient subdiffusion with specific exponents, and relates these findings to nonlinear lattices and high-dimensional restricted diffusion.

Findings

Few-body interactions cause transient subdiffusion with exponents ~0.5 for two and three particles.

Three-body interactions reduce the subdiffusion exponent to approximately 0.2.

Wave packet tails show exponential localization with a slowly decreasing exponent.

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.