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Anderson localization and wave absorption

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Abstract

Experimental signatures of classical wave localization in the absence and in the presence of attenuation are analyzed. The different regimes of the attenuation, reflection, and transmission coefficients for the “diffusive” and “localized” regimes are discussed. Apparent contradictory results presented previously by John and Anderson on the renormalization of absorption by localization are reconciled and shown to apply to different situations.

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References

  1. A. Ishimaru,Wave Propagation in Random Media (Academic Press, New York, 1978).

    Google Scholar 

  2. B. Souillard, Waves and electrons in non-homogeneous media, inProceeding of Les Houches, Session XLVI Chance and Matter, J. Vannimenus, J. Souletie, and R. Stora, eds. (Elsevier, 1987).

  3. D. Sornette, Acoustic waves in random media, II Coherent effects and strong disorder regime,Acustica 67:251 (1989).

    Google Scholar 

  4. P. Lee and T. V. Ramakrishnan,Rev. Mod. Phys. 57:291 (1985); D. Thouless, inIll-Condensed Matter, R. Balian, R. Maynard, and G. Toulouse, eds. (North-Holland, 1979), pp. 1–62; D. Sornette and B. Souillard, A mean field approach to Anderson localization, in preparation.

    Google Scholar 

  5. D. Voohardt and P. Wôffle,Phys. Rev. Lett. 45:842 (1980);48:699 (1982).

    Google Scholar 

  6. E. Guazzelli, E. Guyon, and B. Souillard,J. Phys. (Paris) Lett. 44:837 (1983); M. Belzons, P. Devillard, F. Dunlop, E. Guazzelli, O. Parodi, and B. Souillard, Localization of surface waves on a rough bottom,Europhys. Lett. 4:909 (1987).

    Google Scholar 

  7. C. Hodges,J. Sound Vib. 82:411 (1982); V. Baluni and J. Willemsen,Phys. Rev. B 31:3358 (1985); T. R. Kirkpatrick,Phys. Rev. B 31:5746 (1985).

    Google Scholar 

  8. C. Depollier, J. Kergomard, and F. Laloe,Ann. Phys. Fr. 11:457 (1986).

    Google Scholar 

  9. D. Escande and B. Souillard,Phys. Rev. Lett. 52:1296 (1984).

    Google Scholar 

  10. S. M. Cohen and C. Machta,Phys. Rev. Lett. 54:2242 (1985); C. A. Condat and T. R. Kirkpatrick,Phys. Rev. B 33:3102 (1986).

    Google Scholar 

  11. P. Sheng and Z. Q. Zhang,Phys. Rev. Lett. 57:1879 (1986); C. A. Condat and T. R. Kirkpatrick,Phys. Rev. Lett. 58:226 (1987); K. Arya, Z. B. Su, and J. L. Birman,Phys. Rev. Lett. 57:2725 (1986).

    Google Scholar 

  12. T. R. Kirkpatrick and J. R. Dorfman, Aspects of localization, inFundamental Problems in Statistical Mechanics VI, E. G. D. Cohen, ed. (Elsevier, 1985).

  13. E. Akkermans, P. E. Wolf, and R. Maynard,Phys. Rev. Lett. 56:1471 (1986).

    Google Scholar 

  14. A. Ladendijk, M. P. Van Albada, and M. B. Van der Mark,Physica 140A:183 (1986).

    Google Scholar 

  15. S. He and J. D. Maynard,Phys. Rev. Lett. 57:3171 (1986).

    Google Scholar 

  16. A. Z. Genack,Phys. Rev. Lett. 58:2043 (1986); G. H. Watson, Jr., P. A. Fleury, and S. L. McCall,Phys. Rev. Lett. 58:945 (1986).

    Google Scholar 

  17. D. Sornette and B. Souillard,Eur. Phys. Lett. 7:269 (1988).

    Google Scholar 

  18. S. John,Phys. Rev. Lett. 53:2169 (1984);Phys. Rev. B 31:304 (1985).

    Google Scholar 

  19. P. W. Anderson,Phil. Mag. 52:505 (1985).

    Google Scholar 

  20. E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan,Phys. Rev. Lett. 42:673 (1979).

    Google Scholar 

  21. C. M. Bender and S. A. Orszag,Advanced Mathematical Methods for Scientists and Engineers (1978).

  22. P. M. Morse and H. Feshbach,Methods of Theoretical Physics (McGrawHill, 1953), Part 1, p. 1.80.

  23. H. Kunz and B. Souillard,Commun. Math. Phys. 78:201 (1980).

    Google Scholar 

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Sornette, D. Anderson localization and wave absorption. J Stat Phys 56, 669–680 (1989). https://doi.org/10.1007/BF01016773

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  • DOI: https://doi.org/10.1007/BF01016773

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