Higher-order localization landscape theory of Anderson localization
Higher-order localization landscape theory of Anderson localization
For a Hamiltonian ${\hat H}$ containing a position-dependent (disordered) potential, we introduce a sequence of landscape functions $u_n(\mathbf{r})$ obeying ${\hat H} u_n(\mathbf{r}) = u_{n-1}(\mathbf{r})$ with $u_0(\mathbf{r}) = 1$. For $n \to \infty$, $1/v_n(\mathbf{r}) = u_{n-1}(\mathbf{r})/u_{n}(\mathbf{r})$ converges to the lowest eigenenergy $E_1$ of ${\hat H}$ whereas $u_{\infty}(\mathbf{r})$ yields the corresponding wave …