Anderson localization for multi-frequency quasi-periodic Jacobi operators

Abstract

<p style='text-indent:20px;'>In this paper, we are concerned with the quasi-periodic Jacobi operators with large potentials on <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{T}^d $\end{document}</tex-math></inline-formula> (<inline-formula><tex-math id="M2">\begin{document}$ d \geq 1 $\end{document}</tex-math></inline-formula>) and establish the positivity and continuity of the Lyapunov exponent by combining the large deviation theorem with the avalanche principle. Moreover, we show that Anderson localization takes place for almost all Diophantine frequencies when the coupling is sufficiently large.</p>