Power-law Localization in 2D, 3D with Off-diagonal Disorder
نویسندگان
چکیده
We describe non-conventional localization of the midband E = 0 state in square and cubic finite bipartite lattices with off-diagonal disorder by solving numerically the linear equations for the corresponding amplitudes. This state is shown to display multifractal fluctuations, having many sparse peaks, and by scaling the participation ratio we obtain its disorder-dependent fractal dimension D2. A logarithmic average correlation function grows as g(r) ∼ η ln r at distance r from the maximum amplitude and is consistent with a typical overall power-law decay |ψ(r)| ∼ r−η where η is proportional to the strength of off-diagonal disorder. 71.23.An; 73.20.Dx; 73.20.Jc Typeset using REVTEX
منابع مشابه
Exponents of the localization length in the 2D Anderson model with off-diagonal disorder
We study Anderson localization in two-dimensional systems with purely off-diagonal disorder. Localization lengths are computed by the transfer-matrix method and their finite-size and scaling properties are investigated. We find various numerically challenging differences to the usual problems with diagonal disorder. In particular, the divergence of the localization lengths close to the band cen...
متن کاملExponents of the localization lengths in the bipartite Andersonmodel with off-diagonal disorder
We investigate the scaling properties of the two-dimensional (2D) Anderson model of localization with purely offdiagonal disorder (random hopping). In particular, we show that for small energies the infinite-size localization lengths as computed from transfer-matrix methods together with finite-size scaling diverge with a power-law behavior. The corresponding exponents seem to depend on the str...
متن کاملPhase diagram of the three-dimensional Anderson model of localization with random hopping
Abstract. We examine the localization properties of the three-dimensional (3D) Anderson Hamiltonian with off-diagonal disorder using the transfer-matrix method (TMM) and finitesize scaling (FSS). The nearest-neighbor hopping elements are chosen randomly according to tij ∈ [c− 1/2, c+1/2]. We find that the off-diagonal disorder is not strong enough to localize all states in the spectrum in contr...
متن کاملLocalization of elastic waves in heterogeneous media with off-diagonal disorder and long-range correlations.
Using the Martin-Siggia-Rose method, we study propagation of acoustic waves in strongly heterogeneous media which are characterized by a broad distribution of the elastic constants. Gaussian-white distributed elastic constants, as well as those with long-range correlations with nondecaying power-law correlation functions, are considered. The study is motivated in part by a recent discovery that...
متن کاملGypsum Dissolution Effects on the Performance of a Large Dam (TECHNICAL NOTE)
Upper Gotvand dam is constructed on the Karun River located in the south west of Iran. In this paper, 2D and 3D models of the dam together with the foundation and abutments were constructed and several seepage analyses were carried out. Then the gypsum veins scattered throughout the foundation ground and also the seepage pattern were included in the models, hence the dissolution law of gypsum, ...
متن کامل