Spectral Dependence of the Degree of Localization in a 1D Disordered System with a Complex Structural Unit

Author(s)
Gleb G. Kozlov

ABSTRACT

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.

We analyze the spectral distribution of localisation in a 1D diagonally disordered chain of fragments each of which consist of

Cite this paper

nullG. Kozlov, "Spectral Dependence of the Degree of Localization in a 1D Disordered System with a Complex Structural Unit,"*Applied Mathematics*, Vol. 2 No. 8, 2011, pp. 965-974. doi: 10.4236/am.2011.28133.

nullG. Kozlov, "Spectral Dependence of the Degree of Localization in a 1D Disordered System with a Complex Structural Unit,"

References

[1] V. L. Berezinsky, “Kinetics of a Quantum Particle in a One-Dimensional Random Potential,” Journal of Experimental and Theoretical Physics, Vol. 65, 1973, pp. 1251-1266.

[2] 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.

[3] 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.

[4] Y. A. Bychkov, “Absence of Sound in One-Dimensional Disordered Crystals,” Journal of Experimental and Theoretical Physics, Vol. 67, 1974, pp. 2323-2325.

[5] I. M. Lifshits, S. A. Gredeskul and L. A. Pastur, “Introduction to the Theory of Disordered Systems,” English Translation, Wiley, New York, 1988.

[6] P. W. Anderson, “Absence of Diffusion in Certain Random Lattices,” Physical Review, Vol. 109, No. 5, 1958, pp. 1492-1505. doi:10.1103/PhysRev.109.1492

[7] 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

[8] D. H. Danlap, H.-L. Wu and P. W. Phillips, “Absence of Localization in a Random-Dimer Model,” Physical Review Letters, Vol. 65, No. 1, 1990, pp. 88-91. doi:10.1103/PhysRevLett.65.88

[9] 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

[10] 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

[11] F. J. Dyson, “The Dynamics of a Disordered Linear Chain,” Physical Review, Vol. 92, No. 6, 1953, pp. 1331-1338. doi:10.1103/PhysRev.92.1331

[12] G. G. Kozlov, “Spectrum and Eigen Functions of the Operator and Strange Attractor’s Density for the Mapping ,” arXiv: 0803. 1920. [math-ph], 2008.

[1] V. L. Berezinsky, “Kinetics of a Quantum Particle in a One-Dimensional Random Potential,” Journal of Experimental and Theoretical Physics, Vol. 65, 1973, pp. 1251-1266.

[2] 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.

[3] 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.

[4] Y. A. Bychkov, “Absence of Sound in One-Dimensional Disordered Crystals,” Journal of Experimental and Theoretical Physics, Vol. 67, 1974, pp. 2323-2325.

[5] I. M. Lifshits, S. A. Gredeskul and L. A. Pastur, “Introduction to the Theory of Disordered Systems,” English Translation, Wiley, New York, 1988.

[6] P. W. Anderson, “Absence of Diffusion in Certain Random Lattices,” Physical Review, Vol. 109, No. 5, 1958, pp. 1492-1505. doi:10.1103/PhysRev.109.1492

[7] 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

[8] D. H. Danlap, H.-L. Wu and P. W. Phillips, “Absence of Localization in a Random-Dimer Model,” Physical Review Letters, Vol. 65, No. 1, 1990, pp. 88-91. doi:10.1103/PhysRevLett.65.88

[9] 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

[10] 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

[11] F. J. Dyson, “The Dynamics of a Disordered Linear Chain,” Physical Review, Vol. 92, No. 6, 1953, pp. 1331-1338. doi:10.1103/PhysRev.92.1331

[12] G. G. Kozlov, “Spectrum and Eigen Functions of the Operator and Strange Attractor’s Density for the Mapping ,” arXiv: 0803. 1920. [math-ph], 2008.