Universal Nonlinear Disordered Wave Packet Subdiffusion: 12 Decades

TL;DR

This paper demonstrates that using a novel quantum walk-based simulation toolbox, they observe persistent universal subdiffusion in nonlinear disordered wave packets over unprecedented timescales, surpassing previous computational limits.

Contribution

They introduce a quantum walk toolbox for ultrafast simulations, enabling the observation of sustained subdiffusion over four additional decades, confirming its universality.

Findings

Subdiffusion persists over times up to 2×10^{12}

Universal subdiffusion behavior confirmed beyond previous computational horizons

Quantum walk toolbox outperforms traditional simulation methods

Abstract

We use a novel unitary map toolbox -- discrete time quantum walks originally designed for quantum computing -- to implement ultrafast computer simulations of extremely slow dynamics in a nonlinear and disordered medium. Previous reports on wave packet spreading in Gross-Pitaevskii lattices observed subdiffusion with the second moment $m_2 \sim t^{1/3}$ (with time in units of a characteristic scale $t_0$) up to the largest computed times of the order of $10^8$. A fundamental question remained as to whether this process can continue ad infinitum, or has to slow down. Current experimental devices are not capable to even reach 1\textpertenthousand ~of the reported computational horizons. With our toolbox, we outperform previous computational results and observe that the universal subdiffusion persists over additional four decades reaching 'astronomic' times $2\cdot 10^{12}$. Such a dramatic extension of previous computational horizons suggests that subdiffusion is universal, and that the toolbox can be efficiently used to assess other hard computational many-body problems.