A simple approach to Anderson localization in one-dimensional disordered lattices

American Journal of Physics

Volumn 72, Issue 2, 2004, Pages 226-230

  Dominguez Adame F ^a   Malyshev, V A ^a,b  

^a UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

^b VAVILOV STATE OPTICAL INSTITUTE   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 1042268244     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.1593660     Document Type: Article

References (24)

1. W. A. Harrison, Solid State Theory (Dover, New York, 1980).
2. J. M. Ziman, Models of Disorder (Cambridge U.P., Cambridge, 1979).
3. P. W. Anderson, "Absence of diffusion in certain random lattices," Phys. Rev. 109, 1492-1505 (1958).
4. For more information on the Nobel prize, see 〈http://www.nobel.se/physics/laureates/1977/〉.
5. N. F. Mott and W. D. Twose, "The theory of impurity conduction," Adv. Phys. 10, 107-163 (1961).
6. E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, "Scaling theory of localization: Absence of quantum diffusion in two dimensions," Phys. Rev. Lett. 42, 673-676 (1979).
7. D. J. Thouless, "Electrons in disordered systems and the theory of localization," Rep. Prog. Phys. 13, 93-142 (1974).
8. P. A. Lee and T. V. Ramakrishnan, "Disordered electronic systems," Rev. Mod. Phys. 57, 287-337 (1985).
9. B. Kramer and A. MacKinnon, "Localization: Theory and experiment," Rep. Prog. Phys. 56, 1469-1564 (1993).
10. J. Frenkel, "On the transformation of light into heat in solids. I," Phys. Rev. 37, 17-44 (1931).
11. A. S. Davydov, Theory of Molecular Excitons (Plenum, New York, 1971).
12. V. M. Agranovich and M. D. Galanin, in Electronic Excitation Energy Transfer in Condensed Matter, edited by V. M. Agranovich and A. A. Maradudin (North-Holland, Amsterdam, 1982).
13. F. Domínguez-Adame, E. Maciá, A. Khan, and C. L. Roy, "LCAO approach to non-relativistic and relativistic Kronig-Penney models," Physica B 212, 67-74 (1995).
14. V. A. Malyshev, "Localization length of a ID exciton and temperature dependence of the radiative lifetime in frozen dye-solutions with J-aggregates," Opt. Spectrosc. 71, 505-506 (1991); "Localization length of one-dimensional exciton and low-temperature behaviour of radiative lifetime of J-aggregated dye solutions," J. Lumin, 55, 225-230 (1993).
15. V. A. Malyshev, "Localization length of a ID exciton and temperature dependence of the radiative lifetime in frozen dye-solutions with J-aggregates," Opt. Spectrosc. 71, 505-506 (1991); "Localization length of one-dimensional exciton and low-temperature behaviour of radiative lifetime of J-aggregated dye solutions," J. Lumin, 55, 225-230 (1993).
16. V. Malyshev and P. Moreno, "Hidden structure of the low-energy spectrum of a one-dimensional localized Frenkel exciton," Phys. Rev. B 51, 14587-14593 (1995).
17. V. A. Malyshev, A. Rodríguez, and F. Domínguez-Adame, "Linear optical properties of one-dimensional Frenkel exciton systems with intersite energy correlations," Phys. Rev. B 60, 14140-14146 (1999).
18. A. V. Malyshev and V. A. Malyshev, "Statistics of low energy levels of a one-dimensional weakly localized Frenkel exciton: A numerical study," Phys. Rev. B 63, 195111 (2001).
19. E. E. Jelley, "Spectral absorption and fluorescence of dyes in the molecular state," Nature (London) 138, 1009-1010 (1936).
20. G. Scheibe, "Über die Veränderung der Absorptionspektren in Lösung und die van der Waalss-chen Kräfte als Ihre Ursache," Angew, Chem. 50, 51 (1937).
21. J-Aggregates, edited by T. Kobayashi (World Scientific, Singapore, 1996).
22. E. W. Knapp, "Lineshapes of molecular aggregates. Exchange narrowing and intersite correlation," Chem. Phys. 85, 73-82 (1984).
23. L. D. Bakalis and J. Knoester, "Linear absorption as a tool to measure the exciton delocalization length in molecular assemblies," J. Lumin. 87, 66-70 (2000).
24. F. Domínguez-Adame and V. A. Malyshev, "Frenkel excitons in one-dimensional random systems with correlated disorder," J. Lumin. 83-84, 61-67 (1999).