We analyze the spectral distribution of localisation in a 1D diagonally disordered chain of fragments each of which consist of m coupled two-level systems. The calculations performed by means of developed perturbation theory for joint statistics of advanced and retarded Green’s functions. We show that this distribution is rather inhomogeneous and reveals spectral regions of weakly localized states with sharp peaks of the localization degree in the centers of these regions.
A. A. Gogolin, V. I. Mel’nikov, E. I. Rashba, “Conductivity in a Disordered One-Dimensional System Induced by Electron-Phonon Interaction,” Journal of Experimental and Theoretical Physics, Vol. 69, 1975, pp. 327-349.
A. A. Gogolin, V. I. Mel’nikov, E. I. Rashba, “Effect of Dispersionless Phonons on the Kinetics of Electrons in a One-Dimensional Conductors,” Journal of Experimental and Theoretical Physics, Vol. 72, 1977, pp. 629-645.
G. G. Kozlov, “Computation of Localisation Degree in the Sence of the Anderson Criterion for a One-Dimensional Diagonally Disordered System,” Theoretical and Mathematical Physics, Vol. 162, No. 2, 2010, pp. 238- 253. doi:10.1007/s11232-010-0019-1
V. A. Malyshev, A. Rodriguez and F. Dominguez-Adame, “Linear Optical Properties of One-Dimensional Frenkel Exciton Systems with Intersite Energy Correlations,” Physical Review B, Vol. 60, No. 20, 1999, pp. 14140-14146. doi:10.1103/PhysRevB.60.14140
F. A. B. F. de Moura and Marcelo L. Lyra, “Delocalization in the 1D Anderson Model with Long- Range Correlated Disorder,” Physical Review Letters, Vol. 81, No. 17, 1998, pp. 3735-3738. doi:10.1103/PhysRevLett.81.3735