# Kolmogorov turbulence defeated by Anderson localization for a Bose-Einstein condensate in a Sinai-oscillator trap

## TL;DR

This paper investigates how Anderson localization can suppress Kolmogorov turbulence in a Bose-Einstein condensate within a Sinai-oscillator trap, revealing a threshold for turbulent energy flow to high energies.

## Contribution

It demonstrates that Anderson localization can inhibit weak wave turbulence in a BEC, identifying the conditions under which energy localization occurs versus turbulent energy transfer.

## Key findings

- Anderson localization prevents energy cascade in certain regimes.
- A critical threshold exists for turbulence to overcome localization.
- The phenomenon can be experimentally studied with ultra cold atoms.

## Abstract

We study the dynamics of a Bose-Einstein condensate in a Sinai-oscillator trap under a monochromatic driving force. Such a trap is formed by a harmonic potential and a repulsive disk located in the center vicinity corresponding to the first experiments of condensate formation by Ketterle group in 1995. We argue that the external driving allows to model the regime of weak wave turbulence with the Kolmogorov energy flow from low to high energies. We show that in a certain regime of weak driving and weak nonlinearity such a turbulent energy flow is defeated by the Anderson localization that leads to localization of energy on low energy modes. A critical threshold is determined above which the turbulent flow to high energies becomes possible. We argue that this phenomenon can be studied with ultra cold atoms in magneto-optical traps.