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Response to an external field of a generalized Langevin equation with stochastic resetting of the memory kernel

Petar Jolakoski1,*, Lasko Basnarkov2,†, Ljupco Kocarev1,2,‡, Aleksandra Popovska-Mitrovikj2,§, Verica Bakeva2,¶, and Trifce Sandev1,3,4,**

  • *Contact author: jolakoskip@manu.edu.mk
  • †Contact author: lasko.basnarkov@finki.ukim.mk
  • ‡Contact author: lkocarev@manu.edu.mk
  • §Contact author: aleksandra.popovska.mitrovikj@finki.ukim.mk
  • Contact author: verica.bakeva@finki.ukim.mk
  • **Contact author: trifce.sandev@manu.edu.mk
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Phys. Rev. E 112, 024120 – Published 18 August, 2025

DOI: https://doi.org/10.1103/7q34-r45f

Abstract

We study a generalized Langevin equation framework that incorporates stochastic resetting of a truncation power-law memory kernel. The inclusion of stochastic resetting enables the emergence of resonance phenomena even in parameter regimes where conventional settings (without resetting) do not exhibit such behavior. Specifically, we explore the response of the system to an external field under three scenarios: (i) a free particle, (ii) a particle in a harmonic potential, and (iii) the effect of truncation in the memory kernel. In each case, the primary focus is on understanding how the resetting mechanism interacts with standard parameters to induce stochastic resonance. In addition, we explore the effect of resetting on the dielectric loss.

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References (75)

  1. P. Langevin, C. R. Acad. Sci. Paris 146, 530 (1908).
  2. R. Metzler and J. Klafter, Phys. Rep. 339, 1 (2000).
  3. E. Barkai, R. Metzler, and J. Klafter, Phys. Rev. E 61, 132 (2000).
  4. R. Metzler, E. Barkai, and J. Klafter, Phys. Rev. Lett. 82, 3563 (1999).
  5. A. N. Kolmogorov, Doklady Akademii Nauk SSSR 26, 115 (1940).
  6. B. B. Mandelbrot and J. W. Van Ness, SIAM Rev. 10, 422 (1968).
  7. E. Lutz, Phys. Rev. E 64, 051106 (2001).
  8. W. Deng and E. Barkai, Phys. Rev. E 79, 011112 (2009).
  9. R. Kubo, M. Toda, and N. Hashitsume, Statistical Physics II: Nonequilibrium Statistical Mechanics (Springer Science & Business Media, Heidelberg, 2012), Vol. 31.
  10. R. Zwanzig, Nonequilibrium Statistical Mechanics (Oxford University Press, Oxford, 2001).
  11. A. D. Viñales and M. A. Desposito, Phys. Rev. E 73, 016111 (2006).
  12. M. A. Desposito and A. D. Viñales, Phys. Rev. E 77, 031123 (2008).
  13. S. Burov and E. Barkai, Phys. Rev. E 78, 031112 (2008).
  14. S. Burov and E. Barkai, Phys. Rev. Lett. 100, 070601 (2008).
  15. S. C. Kou and X. S. Xie, Phys. Rev. Lett. 93, 180603 (2004).
  16. S. C. Kou, Ann. Appl. Stat. 2, 501 (2008).
  17. W. Min, G. Luo, B. J. Cherayil, S. C. Kou, and X. S. Xie, Phys. Rev. Lett. 94, 198302 (2005).
  18. I. Goychuk, Phys. Rev. E 80, 046125 (2009).
  19. I. Goychuk, Adv. Chem. Phys. 150, 187 (2012).
  20. G. R. Kneller, K. Baczynski, and M. Pasenkiewicz-Gierula, J. Chem. Phys. 135, 141105 (2011).
  21. J.-H. Jeon, V. Tejedor, S. Burov, E. Barkai, C. Selhuber-Unkel, K. Berg-Sørensen, L. Oddershede, and R. Metzler, Phys. Rev. Lett. 106, 048103 (2011).
  22. J.-H. Jeon, Hector Martinez-Seara Monne, M. Javanainen, and R. Metzler, Phys. Rev. Lett. 109, 188103 (2012).
  23. S. C. Weber, A. J. Spakowitz, and J. A. Theriot, Phys. Rev. Lett. 104, 238102 (2010).
  24. M. R. Evans and S. N. Majumdar, Phys. Rev. Lett. 106, 160601 (2011).
  25. M. R. Evans, S. N. Majumdar, and G. Schehr, J. Phys. A: Math. Theor. 53, 193001 (2020).
  26. O. Tal-Friedman, A. Pal, A. Sekhon, S. Reuveni, and Y. Roichman, J. Phys. Chem. Lett. 11, 7350 (2020).
  27. B. Besga, A. Bovon, A. Petrosyan, S. N. Majumdar, and S. Ciliberto, Phys. Rev. Res. 2, 032029(R) (2020).
  28. S. N. Majumdar, S. Sabhapandit, and G. Schehr, Phys. Rev. E 91, 052131 (2015).
  29. M. Lenzi, E. Lenzi, L. Guilherme, L. Evangelista, and H. Ribeiro, Physica A 588, 126560 (2022).
  30. T. Sandev, V. Domazetoski, L. Kocarev, R. Metzler, and A. Chechkin, J. Phys. A: Math. Theor. 55, 074003 (2022).
  31. S. Ray, Phys. Rev. E 106, 034133 (2022).
  32. A. Pal, V. Stojkoski, and T. Sandev, in Target Search Problems (Springer Nature, Cham, 2024), pp. 323–355.
  33. V. Stojkoski, T. Sandev, L. Kocarev, and A. Pal, Phys. Rev. E 104, 014121 (2021).
  34. D. Vinod, A. G. Cherstvy, W. Wang, R. Metzler, and I. M. Sokolov, Phys. Rev. E 105, L012106 (2022).
  35. D. Vinod, A. G. Cherstvy, R. Metzler, and I. M. Sokolov, Phys. Rev. E 106, 034137 (2022).
  36. A. P. Riascos, D. Boyer, P. Herringer, and J. L. Mateos, Phys. Rev. E 101, 062147 (2020).
  37. F. Huang and H. Chen, Phys. Rev. E 103, 062132 (2021).
  38. A. G. Guerrero-Estrada, A. P. Riascos, and D. Boyer, Chaos 35, 013117 (2025).
  39. T. M. Michelitsch, G. D'Onofrio, F. Polito, and A. P. Riascos, Chaos 35, 013119 (2025).
  40. B. Mukherjee, K. Sengupta, and S. N. Majumdar, Phys. Rev. B 98, 104309 (2018).
  41. R. Yin and E. Barkai, Phys. Rev. Lett. 130, 050802 (2023).
  42. M. Kulkarni and S. N. Majumdar, Phys. Rev. A 108, 062210 (2023).
  43. A. Biswas, J. L. Dubbeldam, T. Sandev, and A. Pal, Chaos 35 (2025).
  44. I. Petreska, L. Pejov, T. Sandev, L. Kocarev, and R. Metzler, Fractal Fractional 6, 88 (2022).
  45. T. Sandev, A. Chechkin, H. Kantz, and R. Metzler, Fractional Calculus Appl. Anal. 18, 1006 (2015).
  46. T. Sandev, I. M. Sokolov, R. Metzler, and A. Chechkin, Chaos, Solitons Fractals 102, 210 (2017).
  47. A. Liemert, T. Sandev, and H. Kantz, Physica A 466, 356 (2017).
  48. T. Sandev, Mathematics 5, 66 (2017).
  49. D. Molina-Garcia, T. Sandev, H. Safdari, G. Pagnini, A. Chechkin, and R. Metzler, New J. Phys. 20, 103027 (2018).
  50. L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, Rev. Mod. Phys. 70, 223 (1998).
  51. Y. P. Kalmykov, W. T. Coffey, and S. V. Titov, J. Magn. Magn. Mater. 265, 44 (2003).
  52. Y. P. Kalmykov, S. V. Titov, D. J. Byrne, W. T. Coffey, M. Zarifakis, and M. H. Al Bayyari, J. Magn. Magn. Mater. 507, 166814 (2020).
  53. Y. P. Kalmykov, B. Ouari, and S. V. Titov, J. Appl. Phys. 120, 053901 (2016).
  54. Y. P. Kalmykov and B. Ouari, Phys. Rev. B 71, 094410 (2005).
  55. Y. P. Kalmykov, S. V. Titov, and W. T. Coffey, Phys. Rev. B 58, 3267 (1998).
  56. P. Jolakoski, P. Trajanovski, A. Pal, V. Stojkoski, L. Kocarev, and T. Sandev, Phys. Rev. E 111, 034129 (2025).
  57. M. R. Evans and S. N. Majumdar, J. Phys. A: Math. Theor. 44, 435001 (2011).
  58. F. Barbi, M. Bologna, and P. Grigolini, Phys. Rev. Lett. 95, 220601 (2005).
  59. I. M. Sokolov and J. Klafter, Phys. Rev. Lett. 97, 140602 (2006).
  60. E. Heinsalu, M. Patriarca, I. Goychuk, and P. Hänggi, Phys. Rev. Lett. 99, 120602 (2007).
  61. E. Barkai and R. Silbey, J. Phys. Chem. B 104, 3866 (2000).
  62. W. T. Coffey, Y. P. Kalmykov, and S. V. Titov, Phys. Rev. E 65, 032102 (2002).
  63. W. T. Coffey, Y. P. Kalmykov, and S. V. Titov, Phys. Rev. E 65, 051105 (2002).
  64. W. Coffey and Y. P. Kalmykov, The Langevin Equation: With Applications to Stochastic Problems in Physics, Chemistry and Electrical Engineering (World Scientific, Singapore, 2012), Vol. 27.
  65. Y. Rocard, J. Phys. Radium 4, 247 (1933).
  66. B. K. P. Scaife, Principles of Dielectrics (Oxford University Press, Oxford, 1998).
  67. W. Gotze and L. Sjogren, Rep. Prog. Phys. 55, 241 (1992).
  68. The repository includes code for the simulations methodology, the code, and corresponding data for plotting the figures, https://github.com/pero-jolak/generalized-langevin-equation.
  69. M. Wiśniewski and J. Spiechowicz, Phys. Rev. E 110, 054117 (2024).
  70. R. Kupferman, J. Stat. Phys. 114, 291 (2004).
  71. C. Tzikang, Determining a Prony series for a viscoelastic material from time varying strain data, Technical report, Langley Research Center, NASA, 2000.
  72. R. H. Byrd, P. Lu, J. Nocedal, and C. Zhu, SIAM J. Sci. Comput. 16, 1190 (1995).
  73. C. Zhu, R. H. Byrd, P. Lu, and J. Nocedal, ACM Trans. Math. Software 23, 550 (1997).
  74. P. Siegle, I. Goychuk, P. Talkner, and P. Hänggi, Phys. Rev. E 81, 011136 (2010).
  75. J. W. Cooley and J. W. Tukey, Math. Comput. 19, 297 (1965).

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Information

Phys. Rev. E 112, 024120– Published 18 August, 2025
  • Received 30 April 2025
  • Accepted 21 July 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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