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First-passage time of run-and-tumble particles with noninstantaneous resetting

Gennaro Tucci1, Andrea Gambassi1, Satya N. Majumdar2, and Grégory Schehr3

  • 1SISSA–International School for Advanced Studies and INFN, via Bonomea 265, I-34136 Trieste, Italy
  • 2LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
  • 3Sorbonne Université, Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589, 4 Place Jussieu, 75252 Paris Cedex 05, France

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Phys. Rev. E 106, 044127 – Published 19 October, 2022

DOI: https://doi.org/10.1103/PhysRevE.106.044127

Abstract

We study the statistics of the first-passage time of a single run-and-tumble particle (RTP) in one spatial dimension, with or without resetting, to a fixed target located at L>0. First, we compute the first-passage time distribution of a free RTP, without resetting or in a confining potential, but averaged over the initial position drawn from an arbitrary distribution p(x). Recent experiments used a noninstantaneous resetting protocol that motivated us to study in particular the case where p(x) corresponds to the stationary non-Boltzmann distribution of an RTP in the presence of a harmonic trap. This distribution p(x) is characterized by a parameter ν>0, which depends on the microscopic parameters of the RTP dynamics. We show that the first-passage time distribution of the free RTP, drawn from this initial distribution, develops interesting singular behaviors, depending on the value of ν. We then switch on resetting, mimicked by relaxation of the RTP in the presence of a harmonic trap. Resetting leads to a finite mean first-passage time and we study this as a function of the resetting rate for different values of the parameters ν and b=L/c, where c is the position of the right edge of the initial distribution p(x). In the diffusive limit of the RTP dynamics, we find a rich phase diagram in the (b,ν) plane, with an interesting reentrance phase transition. Away from the diffusive limit, qualitatively similar rich behaviors emerge for the full RTP dynamics.

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References (83)

  1. O. Bénichou, C. Loverdo, M. Moreau, and R. Voituriez, Rev. Mod. Phys. 83, 81 (2011).
  2. M. R. Evans, S. N. Majumdar, and G. Schehr, J. Phys. A: Math. Theor. 53, 193001 (2020).
  3. M. Villen-Altamirano and J. Villen-Altamirano, RESTART: A method for accelerating rare event simulations, in ITC-13 Workshops : Proceedings of the Thirteenth International Teletraffic Congress, Copenhagen, Denmark, June 19–26, 1991 (North-Holland, Amsterdam, 1991), pp. 71–76.
  4. M. Luby, A. Sinclair, and D. Zuckerman, Inf. Process. Lett. 47, 173 (1993).
  5. A. Montanari and R. Zecchina, Phys. Rev. Lett. 88, 178701 (2002).
  6. H. Tong, C. Faloutsos, and J.-Y. Pan, Knowl. Inf. Syst. 14, 327 (2008).
  7. K. Avrachenkov, A. Piunovskiy, and Y. Zhang, J. Appl. Probab. 50, 960 (2013).
  8. J.-H. Lorenz, International Conference on Current Trends in Theory and Practice of Informatics (Springer, Berlin, 2018), p. 493.
  9. S. Reuveni, M. Urbakh, and J. Klafter, Proc. Natl. Acad. Sci. USA 111, 4391 (2014).
  10. T. Rotbart, S. Reuveni, and M. Urbakh, Phys. Rev. E 92, 060101(R) (2015).
  11. M. Sarkar and S. Gupta, Chaos 32, 073109 (2022).
  12. S. Ray, J. Chem. Phys. 153, 234904 (2020).
  13. T. Sandev, V. Domazetoski, L. Kocarev, R. Metzler, and A. Chechkin, J. Phys. A: Math. Theor. 55, 074003 (2022).
  14. D. Boyer and C. Solis-Salas, Phys. Rev. Lett. 112, 240601 (2014).
  15. S. N. Majumdar, S. Sabhapandit, and G. Schehr, Phys. Rev. E 92, 052126 (2015).
  16. G. Mercado-Vásquez and D. Boyer, J. Phys. A: Math. Theor. 51, 405601 (2018).
  17. A. Masó-Puigdellosas, D. Campos, and V. Méndez, Front. Phys. 7, 112 (2019).
  18. A. Pal, Ł. Kuśmierz, and S. Reuveni, Phys. Rev. Res. 2, 043174 (2020).
  19. C. A. Plata, D. Gupta, and S. Azaele, Phys. Rev. E 102, 052116 (2020).
  20. S. Y. Ali, N. Choudhury, and D. Mondal, J. Phys. A: Math. Theor. 55, 301001 (2022).
  21. B. Levikson, J. Appl. Probab. 14, 492 (1977).
  22. S. C. Manrubia and D. H. Zanette, Phys. Rev. E 59, 4945 (1999).
  23. P. Visco, R. J. Allen, S. N. Majumdar, and M. R. Evans, Biophys. J. 98, 1099 (2010).
  24. M. R. Evans and S. N. Majumdar, Phys. Rev. Lett. 106, 160601 (2011).
  25. M. R. Evans and S. N. Majumdar, J. Phys. A: Math. Theor. 44, 435001 (2011).
  26. M. R. Evans, S. N. Majumdar, and K. Mallick, J. Phys. A: Math. Theor. 46, 185001 (2013).
  27. L. Kusmierz, S. N. Majumdar, S. Sabhapandit, and G. Schehr, Phys. Rev. Lett. 113, 220602 (2014).
  28. S. N. Majumdar, S. Sabhapandit, and G. Schehr, Phys. Rev. E 91, 052131 (2015).
  29. U. Bhat, C. De Bacco, and S. Redner, J. Stat. Mech.: Theory Exp. (2016) 083401.
  30. A. Pal and S. Reuveni, Phys. Rev. Lett. 118, 030603 (2017).
  31. A. Chechkin and I. M. Sokolov, Phys. Rev. Lett. 121, 050601 (2018).
  32. Ł. Kuśmierz and T. Toyoizumi, Phys. Rev. E 100, 032110 (2019).
  33. S. Belan, Phys. Rev. Lett. 120, 080601 (2018).
  34. B. De Bruyne, J. Randon-Furling, and S. Redner, Phys. Rev. Lett. 125, 050602 (2020).
  35. É. Roldán, A. Lisica, D. Sánchez-Taltavull, and S. W. Grill, Phys. Rev. E 93, 062411 (2016).
  36. G. Tucci, A. Gambassi, S. Gupta, and É. Roldán, Phys. Rev. Res. 2, 043138 (2020).
  37. B. De Bruyne and F. Mori, arXiv:2112.11416.
  38. S. Ray, D. Mondal, and S. Reuveni, J. Phys. A: Math. Theor. 52, 255002 (2019).
  39. S. Ahmad, I. Nayak, A. Bansal, A. Nandi, and D. Das, Phys. Rev. E 99, 022130 (2019).
  40. A. Pal and V. V. Prasad, Phys. Rev. Res. 1, 032001(R) (2019).
  41. S. Ray and S. Reuveni, J. Chem. Phys. 152, 234110 (2020).
  42. S. Ray and S. Reuveni, J. Chem. Phys. 154, 171103 (2021).
  43. O. Tal-Friedman, A. Pal, A. Sekhon, S. Reuveni, and Y. Roichman, J. Phys. Chem. Lett. 11, 7350 (2020).
  44. B. Besga, A. Bovon, A. Petrosyan, S. N. Majumdar, and S. Ciliberto, Phys. Rev. Res. 2, 032029(R) (2020).
  45. B. Besga, F. Faisant, A. Petrosyan, S. Ciliberto, and S. N. Majumdar, Phys. Rev. E 104, L012102 (2021).
  46. F. Faisant, B. Besga, A. Petrosyan, S. Ciliberto, and S. N. Majumdar, J. Stat. Mech.: Theory Exp. (2021) 113203.
  47. S. Reuveni, Phys. Rev. Lett. 116, 170601 (2016).
  48. M. R. Evans and S. N. Majumdar, J. Phys. A: Math. Theor. 52, 01LT01 (2019).
  49. A. Pal, Ł. Kuśmierz, and S. Reuveni, Phys. Rev. E 100, 040101(R) (2019).
  50. A. Pal, Ł. Kuśmierz, and S. Reuveni, New J. Phys. 21, 113024 (2019).
  51. D. Gupta, C. A. Plata, and A. Pal, Phys. Rev. Lett. 124, 110608 (2020).
  52. A. S. Bodrova and I. M. Sokolov, Phys. Rev. E 101, 052130 (2020).
  53. D. Gupta, C. A. Plata, A. Kundu, and A. Pal, J. Phys. A: Math. Theor. 54, 025003 (2021).
  54. D. Gupta, A. Pal, and A. Kundu, J. Stat. Mech.: Theory Exp. (2021) 043202.
  55. P. Xu, T. Zhou, R. Metzler, and W. Deng, New J. Phys. 24, 033003 (2022).
  56. G. Mercado-Vásquez, D. Boyer, S. N. Majumdar, and G. Schehr, J. Stat. Mech.: Theory Exp. (2020) 113203.
  57. S. Redner, A Guide to First-Passage Processes (Cambridge University Press, Cambridge, UK, 2001).
  58. A. J. Bray, S. N. Majumdar, and G. Schehr, Adv. Phys. 62, 225 (2013).
  59. H. C. Berg, E. coli in Motion (Springer Science & Business Media, 2008).
  60. J. Tailleur and M. E. Cates, Phys. Rev. Lett. 100, 218103 (2008).
  61. R. W. Nash, R. Adhikari, J. Tailleur, and M. E. Cates, Phys. Rev. Lett. 104, 258101 (2010).
  62. J. Elgeti and G. Gompper, Europhys. Lett. 109, 58003 (2015).
  63. A. P. Solon, M. E. Cates, and J. Tailleur, Eur. Phys. J.: Spec. Top. 224, 1231 (2015).
  64. M. E. Cates and J. Tailleur, Europhys. Lett. 101, 20010 (2013).
  65. E. Orsingher, Stochastic Process. Appl. 34, 49 (1990).
  66. P. Hänggi and P. Jung, Adv. Chem. Phys. 89, 239 (1995).
  67. G. H. Weiss, Physica A 311, 381 (2002).
  68. K. Malakar, V. Jemseena, A. Kundu, K. V. Kumar, S. Sabhapandit, S. N. Majumdar, S. Redner, and A. Dhar, J. Stat. Mech.: Theory Exp. (2018) 043215.
  69. B. De Bruyne, S. N. Majumdar, and G. Schehr, J. Stat. Mech.: Theory Exp. (2021) 043211.
  70. L. Angelani, J. Phys. A: Math. Theor. 48, 495003 (2015).
  71. M. R. Evans and S. N. Majumdar, J. Phys. A: Math. Theor. 51, 475003 (2018).
  72. J. Masoliver, Phys. Rev. E 99, 012121 (2019).
  73. P. C. Bressloff, J. Phys. A: Math. Theor. 53, 105001 (2020).
  74. I. Santra, U. Basu, and S. Sabhapandit, J. Stat. Mech.: Theory Exp. (2020) 113206.
  75. M. Kac, Rocky Mt. J. Math. 4, 497 (1974).
  76. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (U.S. Government Printing Office, Washington, DC, 1948), Vol. 55.
  77. P. Le Doussal, S. N. Majumdar, and G. Schehr, Phys. Rev. E 100, 012113 (2019).
  78. V. Klyatskin, Radiophys. Quantum Electron. 20, 382 (1977).
  79. K. Kitahara, W. Horsthemke, R. Lefever, and Y. Inaba, Prog. Theor. Phys. 64, 1233 (1980).
  80. A. P. Solon, Y. Fily, A. Baskaran, M. E. Cates, Y. Kafri, M. Kardar, and J. Tailleur, Nat. Phys. 11, 673 (2015).
  81. A. Dhar, A. Kundu, S. N. Majumdar, S. Sabhapandit, and G. Schehr, Phys. Rev. E 99, 032132 (2019).
  82. T. Demaerel and C. Maes, Phys. Rev. E 97, 032604 (2018).
  83. A. Pal, A. Kundu, and M. R. Evans, J. Phys. A: Math. Theor. 49, 225001 (2016).

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Phys. Rev. E 106, 044127– Published 19 October, 2022
  • Received 4 April 2022
  • Accepted 9 September 2022
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