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Universal properties of Wigner delay times and resonance widths of tight-binding random graphs

K. B. Hidalgo-Castro1, L. A. Razo-López2,3, A. M. Martínez-Argüello1,*, and J. A. Méndez-Bermúdez1,4

  • *Contact author: blitzkriegheinkel@gmail.com
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Phys. Rev. E 111, 044312 – Published 17 April, 2025

DOI: https://doi.org/10.1103/PhysRevE.111.044312

Abstract

The delay experienced by a probe due to interactions with a scattering media is highly related to the internal dynamics inside that media. This property is well captured by the Wigner delay time and the resonance widths. By the use of the equivalence between the adjacency matrix of a random graph and the tight-binding Hamiltonian of the corresponding electronic media, the scattering matrix approach to electronic transport is used to compute Wigner delay times and resonance widths of Erdős-Rényi graphs and random geometric graphs, including bipartite random geometric graphs. In particular, the situation when a single-channel lead attached to the graphs is considered. Our results show a smooth crossover towards universality as the graphs become complete. We also introduce a parameter ξ, depending on the graph average degree 〈k〉 and graph size N, that scales the distributions of both Wigner delay times and resonance widths, highlighting the universal character of both distributions. Specifically, ξ=〈k〉N−α where α is graph-model dependent.

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References (66)

  1. S. H. Strogatz, Nature (London) 410, 268 (2001).
  2. S. N. Dorogovtsev and J. F. F. Mendes, Adv. Phys. 51, 1079 (2002).
  3. R. Albert and A. L. Barabási, Rev. Mod. Phys. 74, 47 (2002).
  4. M. E. J. Newman, SIAM Rev. 45, 167 (2003).
  5. S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D.-U. Hwang, Phys. Rep. 424, 175 (2006).
  6. R. Durret, Random Graph Dynamics (Cambridge University Press, Cambridge, 2007).
  7. V. Latora, V. Nicosia, and G. Russo, Complex Networks Principles, Methods and Applications (Cambridge University Press, Cambridge, 2017).
  8. E. Estrada, The Structure of Complex Networks: Theory and Applications (Oxford University Press, New York, 2011).
  9. M. Penrose, Random Geometric Graphs (Oxford University Press, New York, 2003).
  10. P. Erdős and A. Rényi, Publ. Math. Debr. 6, 290 (1959).
  11. G. Cimini, T. Squartini, F. Saracco, D. Garlaschelli, A. Gabrielli, and G. Caldarelli, Nat. Rev. Phys. 1, 58 (2019).
  12. A. Ozkanlar and A. E. Clark, J. Comput. Chem. 35, 495 (2014).
  13. S. N. Dorogovtsev, A. V. Goltsev, and J. F. F. Mendes, Rev. Mod. Phys. 80, 1275 (2008).
  14. E. Estrada, N. Hatano, and M. Benzi, Phys. Rep. 514, 89 (2012).
  15. A. L. Barabási and R. Albert, Science 286, 509 (1999).
  16. D. S. Callaway, M. E. J. Newman, S. H. Strogatz, and D. J. Watts, Phys. Rev. Lett. 85, 5468 (2000).
  17. K.-I. Goh, B. Kahng, and D. Kim, Phys. Rev. E 64, 051903 (2001).
  18. G. J. Rodgers, K. Austin, B. Kahng, and D. Kim, J. Phys. A: Math. Gen. 38, 9431 (2005).
  19. B. Georgeot, O. Giraud, and D. L. Shepelyansky, Phys. Rev. E 81, 056109 (2010).
  20. S. Jalan, G. Zhu, and B. Li, Phys. Rev. E 84, 046107 (2011).
  21. I. Farkas, I. Derényi, H. Jeong, Z. Néda, Z. N. Oltvai, E. Ravasz, A. Schubert, A. L. Barabási, and T. Vicsek, Phys. A Stat. Mech. Appl. 314, 25 (2002).
  22. S. N. Dorogovtsev, A. V. Goltsev, J. F. F. Mendes, and A. N. Samukhin, Phys. Rev. E 68, 046109 (2003).
  23. E. López, S. V. Buldyrev, S. Havlin, and H. E. Stanley, Phys. Rev. Lett. 94, 248701 (2005).
  24. Y. H. Xue, J. Wang, L. Li, D. He, and B. Hu, Phys. Rev. E 81, 037101 (2010).
  25. A. J. Martínez-Mendoza, A. Alcazar-López, and J. A. Méndez-Bermúdez, Phys. Rev. E 88, 012126 (2013).
  26. A. M. Martínez-Argüello, K. B. Hidalgo-Castro, and J. A. Méndez-Bermúdez, J. Stat. Mech. (2025) 013303.
  27. R. Aguilar-Sánchez, J. A. Méndez-Bermúdez, F. A. Rodrigues, and J. M. Sigarreta, Phys. Rev. E 102, 042306 (2020).
  28. M. Sade, T. Kalisky, S. Havlin, and R. Berkovits, Phys. Rev. E 72, 066123 (2005).
  29. J. N. Bandyopadhyay and S. Jalan, Phys. Rev. E 76, 026109 (2007).
  30. S. Jalan and J. N. Bandyopadhyay, Phys. Rev. E 76, 046107 (2007).
  31. S. Jalan, N. Solymosi, G. Vattay, and B. Li, Phys. Rev. E 81, 046118 (2010).
  32. C. W. J. Beenakker, Rev. Mod. Phys. 69, 731 (1997).
  33. E. P. Wigner, Phys. Rev. 98, 145 (1955).
  34. F. T. Smith, Phys. Rev. 118, 349 (1960).
  35. Y. V. Fyodorov and H.-J. Sommers, J. Math. Phys. 38, 1918 (1997).
  36. Y. V. Fyodorov, D. V. Savin, and H.-J. Sommers, Phys. Rev. E 55, R4857(R) (1997).
  37. A. M. Martínez-Argüello, A. A. Fernández-Marín, and M. Martínez-Mares, Eur. Phys. J. Spec. Top. 226, 519 (2017).
  38. Y. V. Fyodorov and D. V. Savin, Phys. Rev. Lett. 108, 184101 (2012).
  39. M. Novaes, Europhys. Lett. 139, 21001 (2022).
  40. L. Chen, S. M. Anlage, and Y. V. Fyodorov, Phys. Rev. E 103, L050203 (2021).
  41. L. Chen, S. M. Anlage, and Y. V. Fyodorov, Phys. Rev. Lett. 127, 204101 (2021).
  42. Y. V. Fyodorov and D. V. Savin, Resonance scattering of Waves in chaotic systems, in The Oxford Handbook of Random Matrix Theory, edited by G. Akemann, J. Baik, and P. Di Francesco (Oxford University Press, Oxford, 2011), pp. 703–722.
  43. T. Kottos and M. Weiss, Phys. Rev. Lett. 89, 056401 (2002).
  44. J. A. Méndez-Bermúdez and T. Kottos, Phys. Rev. B 72, 064108 (2005).
  45. A. M. Martínez-Argüello, M. Carrera-Núñez, and J. A. Méndez-Bermúdez, Phys. Rev. E 107, 024139 (2023).
  46. C. Zhong, S. M. Arisona, X. Huang, M. Batty, and G. Schmitt, Int. J. Geogr. Inf. Sci. 28, 2178 (2014).
  47. C. Stegehuis and L. Weedage, Physica A 586, 126460 (2022).
  48. M. Barthélemy, Phys. Rep. 499, 1 (2011).
  49. U. Kuhl, S. Barkhofen, T. Tudorovskiy, H.-J. Stöckmann, T. Hossain, L. de Forges de Parny, and F. Mortessagne, Phys. Rev. B 82, 094308 (2010).
  50. S. Bittner, B. Dietz, M. Miski-Oglu, P. Oria Iriarte, A. Richter, and F. Schäfer, Phys. Rev. B 82, 014301 (2010).
  51. M. Bellec, U. Kuhl, G. Montambaux, and F. Mortessagne, Phys. Rev. B 88, 115437 (2013).
  52. S. Barkhofen, M. Bellec, U. Kuhl, and F. Mortessagne, Phys. Rev. B 87, 035101 (2013).
  53. G. J. Aubry, L. S. Froufe-Pérez, U. Kuhl, O. Legrand, F. Scheffold, and F. Mortessagne, Phys. Rev. Lett. 125, 127402 (2020).
  54. J. Dall and M. Christensen, Phys. Rev. E 66, 016121 (2002).
  55. J. J. M. Verbaarschot, H. A. Weidenmüller, and M. R. Zirnbauer, Phys. Rep. 129, 367 (1985).
  56. A. Ossipov and Y. V. Fyodorov, Phys. Rev. B 71, 125133 (2005).
  57. H. Feshbach, Topics in the theory of nuclear reactions, in Reaction Dynamics, edited by E. W. Montroll, G. H. Vineyard, M. Levy, and P. T. Matthews, (Gordon and Breach, New York, 1973), pp. 32–58.
  58. P. W. Brouwer and C. W. J. Beenakker, Phys. Rev. B 55, 4695 (1997).
  59. F. Steinbach, A. Ossipov, T. Kottos, and T. Geisel, Phys. Rev. Lett. 85, 4426 (2000).
  60. H.-J. Sommers, Y. V. Fyodorov, and M. Titov, J. Phys. A: Math. Gen. 32, L77 (1999).
  61. Y. V. Fyodorov and M. Osman, J. Phys. A: Math. Theor. 55, 224013 (2022).
  62. A. D. Mirlin and Y. V. Fyodorov, J. Phys. A: Math. Gen. 24, 2273 (1991).
  63. Y. V. Fyodorov and A. D. Mirlin, Phys. Rev. Lett. 67, 2049 (1991).
  64. Y. V. Fyodorov and A. D. Mirlin, Phys. Rev. B 55, R16001 (1997).
  65. K. Peralta-Martínez and J. A. Méndez-Bermúdez, J. Phys. Complex. 4, 015002 (2023).
  66. P. W. Brouwer, K. M. Frahm, and C. W. J. Beenakker, Phys. Rev. Lett. 78, 4737 (1997).

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Information

Phys. Rev. E 111, 044312– Published 17 April, 2025
  • Received 20 November 2024
  • Revised 4 April 2025
  • Accepted 8 April 2025
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