Absence of eigenvalues of analytic quasi-periodic Schrodinger operators on ${\mathbb{R}}^d$

In this paper we study on $L^2({\mathbb{R}}^d)$ the quasi-periodic Schr"odinger operator $H=-\mathrm{\Delta }+\lambda V(x),$ where $V$ is a real analytic quasi-periodic function and $\lambda >0$. We first show that $H$ has no eigenvalues in $\mathit{\text{low}}\mathit{\text{energy}}\mathit{\text{region}}$. We also provide in \textit{low energy region} the new phase transition parameter, i.e. the competition between the strength of coupling and the length for frequencies.