corresponds to $F=\frac{2}{5}$ and $V_0= 20 E_r$. In (b) the black line corresponds to $F=\frac{49}{50}$ and $V_0=0.02 E_r$, while the red line corresponds to $F=1$ and $V_0=0.02 E_r$. The dashed black line indicates $\langle K \rangle/N=0$.[]{data-label="fig:currentasfunctionofspeed"}](currentsasfunctionofspeed.pdf){width="\linewidth"}

It was shown by Schenke [*et al.*]{} [@Schenke2012] that persistent currents can be created in a TG gas by driving it with a rotating delta-barrier. If the driving momentum is $q = \eta \pi / L$, where $\eta$ is an integer, this yields maxima in the time-averaged average momentum per particle $\langle K \rangle/N$, while outside these values it stays essentially zero. A similar resonant behaviour is also present in our system when rotating the lattice potential at small lattice depths and for incommensurate filling (see black curve in Fig. \[fig:currentasfunctionofspeed\]), however, the momentum no longer vanishes away from the resonance values. In fact it oscillates between positive and negative momentum with a small amplitude. In order to simplify the discussion in this section we define the scaled driving momentum $\Omega=q L /\pi$. For $F=1$ the values of $\langle K \rangle/N$ around $\Omega= 2 \eta+1$ become large, while the same behavior can be seen for $F=\frac{49}{50}$ around $\Omega= 2 \eta$. This can be understood 