Selective transport in systems with correlated disorder

N.M. Makarov

Instituto de Ciencias, Universidad Autónoma de Puebla, Priv. 17 Norte No 3417, Col. San Miguel Hueyotlipan, Puebla, Pue., 72050, México, e–mail: makarov@siu.buap.mx

Recibido el 14 de diciembre de 2007
Aceptado el 29 de noviembre de 2007

Abstract

We analyze the recent results concerning the anomalous localization properties of one–dimensional and quasi–one–dimensional guiding structures with stratified and surface disorder. The main focus of our study is the role of long–range correlations in random scattering. It is shown that with a proper type of correlations, one can construct a stratification or surface profile that results in a complete transmission/reflection within a prescribed region of the wave number of incoming classical or quantum waves.

Keywords: Anderson localization; correlated disorder; random stratification; rough surface.

Resumen

Se analizan resultados recientes sobre las propiedades de localización anómala de estructuras de guías de onda uni– y cuasiunidimensionales con desorden estratificado y superficial. El punto principal de estudio es el papel que desempenan las correlaciones de largo alcance en el esparcimiento aleatorio. Se demuestra que uno puede construir, con el tipo apropiado de correlaciones, una estratificacion o perfil superficial que den una transmisión/reflexión completa en una región prescrita del número de onda de las ondas clásicas o cuánticas entrantes.

Descriptores: Localización de Anderson; desorden correlacionado; estratificación aleatoria; superficie rugosa.

PACS: 42.25.Dd; 72.10.–d; 72.15.Rn; 73.20.Fz

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References

1. F. Moura and M.L. Lyra, Phys. Rev. Lett. 81 (1998) 3735.        [ Links ]

2. F.M. Izrailev, A.A. Krokhin, Phys. Rev. Lett. 82 (1999) 4062;         [ Links ] A.A. Krokhin, F.M. Izrailev, Ann. Phys. (Leipzig) SI–8 (1999) 153.        [ Links ]

3. F.M. Izrailev, A.A. Krokhin, and S.E. Ulloa, Phys. Rev. B 63 (2001) 041102 (R).        [ Links ]

4. U. Kuhl, F.M. Izrailev, A.A. Krokhin, and H.–J. Stöckmann, Appl. Phys. Lett. 77 (2000) 633;         [ Links ] A. Krokhin, F. Izrailev, U. Kuhl, H.–J. Stöckmann, and S.E. Ulloa, Physica E 13 (2002) 695.        [ Links ]

5. F.M. Izrailev, N.M. Makarov, Opt. Lett. 26 (2001) 1604.        [ Links ]

6. F.M. Izrailev and N.M. Makarov, Phys. Rev. B 67 (2003) 113402.        [ Links ]

7. F.M. Izrailev and N.M. Makarov, Phys. Stat. Sol. (c) 0 (2003) 3037.        [ Links ]

8. F.M. Izrailev and N.M. Makarov, Appl. Phys. Lett. 84 (2004) 5150.        [ Links ]

9. N.M. Makarov and F.M. Izrailev, Proc. Fifth Int. Kharkov Symposium on Physics and Engineering of Microwaves, Millimeter, and Submillimeter Waves (Kharkov, Ukraine, 2004) vol 1, p 122–127, IEEE Catalog Number: 04EX828, ISBN: 0–7803–8411–3, Library of Congress: 2004102369.        [ Links ]

10. N.M. Makarov, F.M. Izrailev, and G. Luna–Acosta, Proc. Sixth Int. Kharkov Symposium on Physics and Engineering of Microwaves, Millimeter, and Submillimeter Waves and Workshop on Terahertz Technologies (Kharkov, Ukraine, 2007) vol 1, p 140–145, IEEE Catalog Number: 07EX1786, ISBN: 1–4244–1237–4, Library of Congress: 2007925116.        [ Links ]

11. F.M. Izrailev and N.M. Makarov, J. Phys. A: Math. Gen. 38 (2005) 10613.        [ Links ]

12. See, for example, I.M. Lifshits, S.A. Gredeskul, and L.A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, New York, 1988);         [ Links ] P.A. Mello and N. Kumar, Quantum Transport in Mesoscopic Systems: Complexity and Statistical Fluctuations (Oxford University Press, Oxford, UK, 2004);         [ Links ] V.I. Klyatskin, Dynamics of Stochastic Systems (Elsevier, Amsterdam, 2005).        [ Links ]

13. N.M. Makarov and I.V Yurkevich, Zh. Eksp. Teor. Fiz. 96 (1989) 1106 (Sov. Phys. JETP 69 (1989) 628));         [ Links ] V.D. Freilikher, N.M. Makarov, and I.V. Yurkevich, Phys. Rev. B 41 (1990) 8033.        [ Links ]

14. N.M. Makarov, Lectures on Spectral and Transport Properties of One–Dimensional Disordered Conductors, 1999 (http://www.ifuap.buap.mx/virtual/pagevir.html).        [ Links ]

15. S.O. Rice, Bell Syst. Tech. J. 23 (1944) 282;         [ Links ] S.O. Rice, in Selected Papers on Noise and Stochastic Processes, ed. by N. Wax (Dover, New York, 1954) p. 180.        [ Links ]

16. D. Saupe, in The Science of Fractal Images, ed. by H.–O. Peitgen and D. Saupe (Springer, New York, 1988);         [ Links ] J. Feder, Fractals (Plenum Press, New York, 1988).        [ Links ]

17. C.S. West and K.A. O'Donnell, J. Opt. Soc. Am. A 12 (1995) 390.        [ Links ]

18. A. Czirok, R.N. Mantegna, S. Havlin, and H.E. Stanley, Phys. Rev. E 52 (1995) 446;         [ Links ] H.A. Makse, S. Havlin, M. Schwartz, and H.E. Stanley, Phys. Rev. E 53 (1996) 5445.        [ Links ]

19. A. Romero and J. Sancho, Journal of Computational Physics 156, (1999) 1;         [ Links ] J. García–Ojalvo and J. Sancho, Noise in Spatially Extended Systems (Springer–Verlag, New York, 1999).        [ Links ]

20. R. Cakir, P. Grigolini, and A.A. Krokhin, Phys. Rev. E 74 (2006) 021108.        [ Links ]

21. F.M. Izrailev, A.A. Krokhin, N.M. Makarov, and O.V. Usatenko, Phys. Rev. E 76 (2007) 027701.        [ Links ]

22. U. Kuhl and H.–J. Stöckmann, Phys. Rev. Lett. 80 (1998) 2323.        [ Links ]

23. V. Bellani et al., Phys. Rev. Lett. 82 (1999) 2159.          [ Links ]

24. J.A. Sánchez –Gil, V. Freilikher, I.V. Yurkevich, and A.A. Maradudin, Phys. Rev. Lett. 80 (1998) 948;         [ Links ] J.A. Sánchez–Gil, V. Freilikher, A.A. Maradudin, and I.V. Yurkevich, Phys. Rev. B 59 (1999) 5915.        [ Links ]