Switch-on drift in a circularly driven parabolic band ($\mathbf{k}=(e{E}_0/\hslash \omega )(\cos \omega t-1,-\sin \omega t)$)

A charge $-e$ starting at a band minimum when the field $E_0(\sin \omega t,\cos \omega t)$ is applied acquires the displayed crystal momentum. Its orbit is a shifted circle. For masses $m_x,m_y$, the real-space coordinates are proportional to $(\sin \omega t-\omega t)/m_x$ and $(\cos \omega t-1)/m_y$: an elliptic oscillation plus a uniform drift. Omitting the integration constant changes the physical initial condition and reduces the maximum light-axis kinetic energy by a factor of four.