Spectral Theory for Nonstationary Random Potentials

Delocalization in one-dimensional tight-binding models with fractal disorder

“…Note that the non-stationarity can be satisfied for α ≥ 1. In addition, the LDT with mobility edges, has been found numerically for the onedimensional tight-binding model with the FFM model as the potential strength W decreases [16,17,18,19,20,21,22].…”

“…The explicit form becomes, C(a, n, m) = < V (n)V (m) > < V (n) 2 > , (17) Figure 11 shows the autocorrelation function C(a = 2, r) given by Eq. (16) for various values of some fractal dimensions. It follows that the correlation function rapidly decays with complex fluctuation for D = 1.9.…”

“…(Color online) The autocorrelation function C(r) as a function of the distance r for various fractal dimension D given by Eq. (16). The parameters are a = 2, N = 2 15 .…”

Some Estimates Regarding Integrated Density of States for Random Schrödinger Operator with Decaying Random Potentials

“…Using a Laplace transform they studied the asymptotic behaviour of the integrated density of surface states for random Gaussian surface potentials. In [6], Bócker-Werner-Stollmann review some results on the spectral theory of non-stationary random potentials (see also [9]). They present various models with decaying and sparse random potentials, including those where the sparse set itself is random.…”

Existence, uniqueness and anisotropic-decay-caused Lifshitz tails of the integrated density of surface states for random surface models

“…A vast amount of literature has been carried out toward the spectral structure on the random Schrödinger operator (1.1) as well as its discrete analog. See [4,5,7,8,18,21,22,23,24] and references therein. However, there is very few work on Lifshitz tails for the random Schrödinger operator (1.1) and its discrete version.…”