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Universal Vibrational Properties of Disordered Systems in Terms of the Theory of Random Correlated Matrices

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Abstract

It has been shown that a correlated Wishart ensemble can be used to study the general vibrational properties of stable amorphous solids, where the energy is translationally invariant. The vibrational density of states and the dynamic structure factor of the system have been determined using the random matrix theory. The results indicate the existence of the Ioffe–Regel crossover between low-frequency propagating phonons and diffusons at higher frequencies. The presented vibrational density of states demonstrates the boson peak at the frequency close to the Ioffe—Regel crossover.

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References

  1. P. B. Allen and J. L. Feldman, Phys. Rev. B 48, 12581 (1993).

    Article  ADS  Google Scholar 

  2. B. Allen, J. L. Feldman, J. Fabian, and F. Wooten, Philos. Mag. B 79, 1715 (1999).

    Article  ADS  Google Scholar 

  3. V. K. Malinovsky and A. P. Sokolov, Solid State Commun. 57, 757 (1986).

    Article  ADS  Google Scholar 

  4. M. Kabeya, T. Mori, Y. Fujii, A. Koreeda, B. W. Lee, J.-H. Ko, and S. Kojima, Phys. Rev. B 94, 224204 (2016).

    Article  ADS  Google Scholar 

  5. P. Benassi, M. Krisch, C. Masciovecchio, V. Mazzacurati, G. Monaco, G. Ruocco, F. Sette, and R. Verbeni, Phys. Rev. Lett. 77, 3835 (1996).

    Article  ADS  Google Scholar 

  6. A. Wischnewski, U. Buchenau, A. J. Dianoux, W. A. Kamitakahara, and J. L. Zarestky, Philos. Mag. B 77, 579 (1998).

    Article  ADS  Google Scholar 

  7. K. Matsuishi, S. Onari, and T. Arai, Jpn. J. Appl. Phys. 25, 1144 (1986).

    Article  ADS  Google Scholar 

  8. K. W. Hutt, W. A. Phillips, and R. J. Butcher, J. Phys.: Condens. Matter 1, 4767 (1989).

    ADS  Google Scholar 

  9. T. Ohsaka and T. Ihara, Phys. Rev. B 50, 9569 (1994).

    Article  ADS  Google Scholar 

  10. R. C. Zeller and R. O. Pohl, Phys. Rev. B 4, 2029 (1971).

    Article  ADS  Google Scholar 

  11. W. A. Phillips, Amorphous Solids: Low-Temperature Properties (Springer, Berlin, 1981).

    Book  Google Scholar 

  12. G. K. White, S. J. Collocott, and J. S. Cook, Phys. Rev. B 29, 4778 (1984).

    Article  ADS  Google Scholar 

  13. S. Kojima, Y. Matsuda, M. Kodama, H. Kawaji, and T. Atake, Chin. J. Phys. 49, 414 (2011).

    Google Scholar 

  14. W. Steurer, A. Apfolter, M. Koch, W. E. Ernst, B. Holst, E. Søndergård, and J. R. Manson, Phys. Rev. Lett. 99, 035503 (2007).

    Article  ADS  Google Scholar 

  15. W. Steurer, A. Apfolter, M. Koch, W. E. Ernst, E. Søndergård, J. R. Manson, and B. Holst, Phys. Rev. B 78, 045427 (2008).

    Article  ADS  Google Scholar 

  16. L. Zhang, J. Zheng, Y. Wang, L. Zhang, Z. Jin, L. Hong, Y. Wang, and J. Zhang, Nat. Commun. 8, 67 (2017).

    Article  ADS  Google Scholar 

  17. Y. Wang, L. Hong, Y. Wang, W. Schirmacher, and J. Zhang, Phys. Rev. B 98, 174207 (2018).

    Article  ADS  Google Scholar 

  18. B. Rufflé, G. Guimbretière, E. Courtens, R. Vacher, and G. Monaco, Phys. Rev. Lett. 96, 045502 (2006).

    Article  ADS  Google Scholar 

  19. B. Rufflé, D. A. Parshin, E. Courtens, and R. Vacher, Phys. Rev. Lett. 100, 015501 (2008).

    Article  ADS  Google Scholar 

  20. H. Shintani and H. Tanaka, Nat. Mater. 7, 870 (2008).

    Article  ADS  Google Scholar 

  21. W. Schirmacher, G. Ruocco, and T. Scopigno, Phys. Rev. Lett. 98, 025501 (2007).

    Article  ADS  Google Scholar 

  22. M. Wyart, Eur. Phys. Lett. 89, 64001 (2010).

    Article  ADS  Google Scholar 

  23. A. Marruzzo, W. Schirmacher, A. Fratalocchi, and G. Ruocco, Sci. Rep. 3, 1407 (2013).

    Article  ADS  Google Scholar 

  24. E. DeGiuli, A. Laversanne-Finot, G. Diring, E. Lern-era, and M. Wyart, Soft Matter 10, 5628 (2014).

    Article  ADS  Google Scholar 

  25. E. DeGiuli, E. Lerner, and M. Wyart, J. Chem. Phys. 142, 164503 (2015).

    Article  ADS  Google Scholar 

  26. V. L. Gurevich, D. A. Parshin, and H. R. Schober, Phys. Rev. B 67, 094203 (2003).

    Article  ADS  Google Scholar 

  27. D. A. Parshin, H. R. Schober, and V. L. Gurevich, Phys. Rev. B 76, 064206 (2007).

    Article  ADS  Google Scholar 

  28. V. G. Karpov, M. I. Klinger, and F. N. Ignat’ev, Sov. Phys. JETP 57, 439 (1983).

    Google Scholar 

  29. U. Buchenau, Yu. M. Galperin, V. L. Gurevich, and H. R. Schober, Phys. Rev. B 43, 5039 (1991).

    Article  ADS  Google Scholar 

  30. U. Buchenau, Yu. M. Galperin, V. L. Gurevich, D. A. Parshin, M. A. Ramos, and H. R. Schober, Phys. Rev. B 46, 2798 (1992).

    Article  ADS  Google Scholar 

  31. W. Götze and M. R. Mayr, Phys. Rev. E 61, 587 (2000).

    Article  ADS  Google Scholar 

  32. S. N. Taraskin, Y. L. Loh, G. Natarajan, and S. R. Elliott, Phys. Rev. Lett. 86, 1255 (2001).

    Article  ADS  Google Scholar 

  33. A. I. Chumakov, G. Monaco, A. Monaco, et al., Phys. Rev. Lett. 106, 225501 (2011).

    Article  ADS  Google Scholar 

  34. H. Shintani and H. Tanaka, Nat. Mater. 7, 870 (2008).

    Article  ADS  Google Scholar 

  35. T. S. Grigera, V. Martin-Mayor, G. Parisi, and P. Verrocchio, J. Phys.: Condens. Matter 14, 2167 (2002).

    ADS  Google Scholar 

  36. M. L. Manning and A. J. Liu, Eur. Phys. Lett. 109, 36002 (2015).

    Article  ADS  Google Scholar 

  37. Y. M. Beltukov, V. I. Kozub, and D. A. Parshin, Phys. Rev. B 87, 134203 (2013).

    Article  ADS  Google Scholar 

  38. M. Baggioli, R. Milkus, and A. Zaccone, Phys. Rev. E 100, 062131 (2019).

    Article  ADS  Google Scholar 

  39. R. Speicher and C. Vargas, Random Matrices: Theory Appl. 1, 1150008 (2012).

    Article  MathSciNet  Google Scholar 

  40. L. Laloux, P. Cizeau, M. Potters, and J.-P. Bouchaud, Int. J. Theor. Appl. Finance 3, 391 (2000).

    Article  Google Scholar 

  41. K. Rajan and L. F. Abbott, Phys. Rev. Lett. 97, 188104 (2006).

    Article  ADS  Google Scholar 

  42. J. Harnad, Random Matrices, Random Processes and Integrable Systems (Springer, New York, 2011).

    Book  MATH  Google Scholar 

  43. A. M. Tulino and S. Verdu, Found. Trends Commun. Inf. Theory 1, 1 (2004).

    Article  Google Scholar 

  44. K. E. Wage, J. Acoust. Soc. Am. 138, 1840 (2015).

    Article  ADS  Google Scholar 

  45. H. Meyer and J. C. Angles d’Auriac, Phys. Rev. E 55, 6608 (1997).

    Article  ADS  Google Scholar 

  46. N. A. Olekhno and Y. M. Beltukov, Phys. Rev. E 97, 050101(R) (2018).

    Article  ADS  Google Scholar 

  47. Ya. M. Beltukov, JETP Lett. 101, 345 (2015).

    Article  ADS  Google Scholar 

  48. A. J. Liu and S. R. Nagel, Ann. Rev. Condens. Matter Phys. 1, 347 (2010).

    Article  ADS  Google Scholar 

  49. C. S. O’Hern, L. E. Silbert, A. J. Liu, and S. R. Nagel, Phys. Rev. E 68, 011306 (2003).

    Article  ADS  Google Scholar 

  50. F. Evers and A. D. Mirlin, Rev. Mod. Phys. 80, 1355 (2008).

    Article  ADS  Google Scholar 

  51. F. J. Dyson, J. Math. Phys. 3, 140 (1962).

    Article  ADS  Google Scholar 

  52. F. J. Dyson, J. Math. Phys. 3, 1199 (1962).

    Article  ADS  Google Scholar 

  53. R. Bhatia, Positive Definite Matrices (Princeton Univ. Press, Princeton, 2007).

    MATH  Google Scholar 

  54. Ya. M. Beltukov and D. A. Parshin, JETP Lett. 104, 552 (2016).

    Article  ADS  Google Scholar 

  55. Z. Burda, A. Görlich, A. Jarosz, and J. Jurkiewicz, Phys. A (Amsterdam, Neth.) 343, 295 (2004).

    Article  ADS  Google Scholar 

  56. F. H. Stillinger and T. A. Weber, Phys. Rev. B 31, 5262 (1985).

    Article  ADS  Google Scholar 

  57. I. J. Zucker, J. Stat. Phys. 145, 591 (2011).

    Article  ADS  MathSciNet  Google Scholar 

  58. Z. Burda, A. Görlich, J. Jurkiewicz, and B. Waclaw, Eur. Phys. J. B 49, 319 (2006).

    Article  ADS  Google Scholar 

  59. V. Vitelli, N. Xu, M. Wyart, A. J. Liu, and S. R. Nagel, Phys. Rev. E 81, 021301 (2010).

    Article  ADS  Google Scholar 

  60. D. A. Conyuh and Ya. M. Beltukov, Phys. Solid State 62, 689 (2020).

    Article  ADS  Google Scholar 

  61. C. Rainone, E. Bouchbinder, and E. Lerner, Proc. Natl. Acad. Sci. U. S. A. 117, 5228 (2020).

    Article  ADS  Google Scholar 

  62. F. Sette, M. H. Krisch, C. Masciovecchio, G. Ruocco, and G. Monaco, Science (Washington, DC, U. S.) 280, 1550 (1998).

    Article  Google Scholar 

  63. G. Ruocco and F. Sette, J. Phys.: Condens. Matter 13, 9141 (2001).

    ADS  Google Scholar 

  64. J. K. Christie, S. N. Taraskin, and S. R. Elliott, J. Non-Cryst. Solids 353, 2272 (2007).

    Article  ADS  Google Scholar 

  65. G. Monaco and S. Mossa, Proc. Natl. Acad. Sci. U.S.A. 106, 16907 (2009).

    Article  ADS  Google Scholar 

  66. H. Mizuno and A. Ikeda, Phys. Rev. E 98, 062612 (2018).

    Article  ADS  Google Scholar 

  67. M. Wyart, L. E. Silbert, S. R. Nagel, and T. A. Witten, Phys. Rev. E 72, 051306 (2005).

    Article  ADS  Google Scholar 

  68. O. Narayan and H. Mathur, arXiv: 2006.16497.

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Acknowledgments

We are grateful to D.A. Parshin and V.I. Kozub for stimulating discussions.

Funding

This work was supported by the Council of the President of the Russian Federation for State Support of Young Scientists and Leading Scientific Schools (project no. MK-3052.2019.2).

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Authors and Affiliations

  1. Ioffe Institute, Russian Academy of Sciences, St. Petersburg, 194021, Russia

    D. A. Conyuh & Y. M. Beltukov

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  1. D. A. Conyuh
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Correspondence to D. A. Conyuh.

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Russian Text © The Author(s), 2020, published in Pis’ma v Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2020, Vol. 112, No. 8, pp. 547–553.

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Conyuh, D.A., Beltukov, Y.M. Universal Vibrational Properties of Disordered Systems in Terms of the Theory of Random Correlated Matrices. Jetp Lett. 112, 513–519 (2020). https://doi.org/10.1134/S0021364020200072

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