- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Universal hyperuniformity in active field theories

Yuanjian Zheng1,*, Michael A. Klatt1,2,3,†, and Hartmut Löwen1,‡

  • *Contact author: zhengy@hhu.de
  • †Contact author: klatt@hhu.de
  • ‡Contact author: hlowen@hhu.de
PDF

Phys. Rev. Research 6, L032056 – Published 6 September, 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.L032056

Abstract

We show that dry scalar-order active field theories (AFTs) are universally hyperuniform, i.e., density fluctuations are anomalously suppressed in the long-time limit regardless of the integrability or functional form of the active contributions up to third order in gradient terms. These AFTs include active model B, active model B+, and effective Cahn-Hilliard models. Moreover, density variances and spectral densities are virtually indistinguishable from that of passive phase-separated hyperuniform fields. Higher moments of the density fluctuations, however, reveal activity-dependent higher-order correlations that are not captured by conventional two-point measures that characterize hyperuniformity.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (59)

  1. M. Marchetti, J. Joanny, S. Ramaswamy, T. Liverpool, J. Prost, M. Rao, and R. A. Simha, Hydrodynamics of soft active matter, Rev. Mod. Phys. 85, 1143 (2013).
  2. C. Bechinger, R. Di Leonardo, H. Löwen, C. Reichhardt, G. Volpe, and G. Volpe, Active particles in complex and crowded environments, Rev. Mod. Phys. 88, 045006 (2016).
  3. S. Ramaswamy, The mechanics and statics of active matter, Annu. Rev. Condens. Matter Phys. 1, 323 (2010).
  4. I. Theurkauff, C. Cottin-Bizonne, J. Palacci, C. Ybert, and L. Bocquet, Dynamic clustering in active colloidal suspensions with chemical signaling, Phys. Rev. Lett. 108, 268303 (2012).
  5. J. Yu, B. Wang, X. Du, Q. Wang, and L. Zhang, Ultra-extensible ribbon-like magnetic microswarm, Nat. Commun. 9, 3260 (2018).
  6. C. Scholz, S. Jahanshahi, A. Ldov, and H. Löwen, Inertial delay of self-propelled particles, Nat. Commun. 9, 5156 (2018).
  7. D. Mandal, K. Klymko, and M. R. DeWeese, Entropy production and fluctuation theorems for active matter, Phys. Rev. Lett. 119, 258001 (2017)
  8. E. Fodor, C. Nardini, M. E. Cates, J. Tailleur, P. Visco, and F. van Wijland, How far from equilibrium is active matter? Phys. Rev. Lett. 117, 038103 (2016).
  9. C. Scheibner, A. Souslov, D. Banerjee, P. Surówka, W. T. M. Irvine, and V. Vitelli, Odd elasticity, Nat. Phys. 16, 475 (2020).
  10. A. Zöttl and H. Stark, Emergent behavior in active colloids, J. Phys.: Condens. Matter 28, 253001 (2016).
  11. J. Schwarz-Linek, C. Valeriani, A. Cacciuto, M. E. Cates, D. Marenduzzo, A. N. Morozov, and W. C. K. Poon, Phase separation and rotor self-assembly in active particle suspensions, Proc. Natl. Acad. Sci. USA 109, 4052 (2012).
  12. M. E. Cates and J. Tailleur, Motility-induced phase separation, Annu. Rev. Condens. Matter Phys. 6, 219 (2015).
  13. Y. Fily and M. C. Marchetti, Athermal phase separation of self-propelled particles with no alignment, Phys. Rev. Lett. 108, 235702 (2012).
  14. G. S. Redner, M. F. Hagan, and A. Baskaran, Structure and dynamics of a phase-separating active colloidal fluid, Phys. Rev. Lett. 110, 055701 (2013).
  15. T. Speck, J. Bialké, A. M. Menzel, and H. Löwen, Effective Cahn-Hilliard equation for the phase separation of active Brownian particles, Phys. Rev. Lett. 112, 218304 (2014).
  16. R. Wittkowski, A. Tiribocchi, J. Stenhammar, R. J. Allen, D. Marenduzzo, and M. E. Cates, Scalar φ4 field theory for active-particle phase separation, Nat. Commun. 5, 4351 (2014).
  17. E. Tjhung, C. Nardini, and M. E. Cates, Cluster phases and bubbly phase separation in active fluids: Reversal of the Ostwald process, Phys. Rev. X 8, 031080 (2018).
  18. M. E. Cates, Active field theories, in Active Matter and Nonequilibrium Statistical Physics: Lecture Notes of the Les Houches Summer School, edited by J. Tailleur, G. Gompper, M. C. Marchetti, J. M. Yeomans, and C. Salomon (Oxford University Press, Oxford, 2022), Vol. 112.
  19. P. C. Hohenberg and B. I. Halperin, Theory of dynamic critical phenomena, Rev. Mod. Phys. 49, 435 (1977).
  20. J. W. Cahn and J. E. Hilliard, Free energy of a nonuniform system. I. Interfacial free energy, J. Chem. Phys. 28, 258 (1958).
  21. J. Zhang, R. Alert, J. Yan, N. S. Wingreen, and S. Granick, Active phase separation by turning towards regions of higher density, Nat. Phys. 17, 961 (2021).
  22. C. Tung, J. Harder, C. Valeriani, and A. Cacciuto, Micro-phase separation in two dimensional suspensions of self-propelled spheres and dumbbells, Soft Matter 12, 555 (2016).
  23. C. Anderson and A. Fernandez-Nieves, Social interactions lead to motility-induced phase separation in fire ants, Nat. Commun. 13, 6710 (2022).
  24. E. Kalz, A. Sharma, and R. Metzler, Field theory of active chiral hard disks: a first-principles approach to steric interactions, J. Phys. A: Math. Theor. 57, 265002 (2024).
  25. Q.-L. Lei, M. P. Ciamarra, and R. Ni, Nonequilibrium strongly hyperuniform fluids of circle active particles with large local density fluctuations, Sci. Adv. 5, eaau7423 (2019).
  26. Q.-L. Lei and R. Ni, Hydrodynamics of random-organizing hyperuniform fluids, Proc. Natl. Acad. Sci. USA 116, 22983 (2019).
  27. S. Torquato, Swimming in circles can lead to exotic hyperuniform states of active living matter, Proc. Natl. Acad. Sci. USA 118, e2016862118 (2021).
  28. M. Huang, W. Hu, S. Yang, and H. P. Zhang, Circular swimming motility and disordered hyperuniform state in an algae system, Proc. Natl. Acad. Sci. USA 118, e2100493118 (2021).
  29. B. Zhang and A. Snezhko, Hyperuniform active chiral fluids with tunable internal structure, Phys. Rev. Lett. 128, 218002 (2022).
  30. N. Oppenheimer, D. B. Stein, M. Y. B. Zion, and M. J. Shelley, Hyperuniformity and phase enrichment in vortex and rotor assemblies, Nat. Commun. 13, 804 (2022).
  31. Y. Kuroda and K. Miyazaki, Microscopic theory for hyperuniformity in two-dimensional chiral active fluid, J. Stat. Mech. (2023) 103203.
  32. S. Torquato and F. H. Stillinger, Local density fluctuations, hyperuniformity, and order metrics, Phys. Rev. E 68, 041113 (2003).
  33. S. Torquato, Hyperuniform states of matter, Phys. Rep. 745, 1 (2018).
  34. S. Torquato, Hyperuniformity and its generalizations, Phys. Rev. E 94, 022122 (2016).
  35. Z. Ma and S. Torquato, Random scalar fields and hyperuniformity, J. Appl. Phys. 121, 244904 (2017).
  36. S. Ramaswamy, R. A. Simha, and J. Toner, Active nematics on a substrate: Giant number fluctuations and long-time tails, Europhys. Lett. 62, 196 (2003).
  37. H. Chaté, F. Ginelli, and R. Montagne, Simple model for active Nematics: Quasi-long-range order and giant fluctuations, Phys. Rev. Lett. 96, 180602 (2006).
  38. V. Narayan, S. Ramaswamy, and N. Menon, Long-lived giant number fluctuations in a swarming granular nematic, Science 317, 105 (2007).
  39. Y. Kuroda and K. Miyazaki, Anomalous fluctuations in homogeneous fluid phase of active Brownian particles, Phys. Rev. Res. 5, 013077 (2023).
  40. X. Ma, J. Pausch, and M. E. Cates, Theory of hyperuniformity at the absorbing state transition, arXiv:2310.17391.
  41. H.-H. Boltz and T. Ihle, Hyperuniformity in deterministic anti-aligning active matter, arXiv:2402.19451.
  42. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing, 3rd ed. (Cambridge University Press, Cambridge, 2007).
  43. S. Wilken, A. Chaderjian, and O. A. Saleh, Spatial organization of phase-separated DNA droplets, Phys. Rev. X 13, 031014 (2023).
  44. Unconstrained fits to the power law–σ2∼a0R−λ for a0 and λ.
  45. The global minimum of ψ(r) for a given AX.
  46. See Supplemental Material http://link.aps.org/supplemental/10.1103/PhysRevResearch.6.L032056 for numerical details and estimates for ξh, λ, l1, k1, and α, as well as measures of goodness of fits, and discussion on the absence of finite-size effects for various AX.
  47. D. Hexner and D. Levine, Noise, diffusion, and hyperuniformity, Phys. Rev. Lett. 118, 020601 (2017).
  48. Y. Zheng, Y.-W. Li, and M. P. Ciamarra, Hyperuniformity and density fluctuations at a rigidity transition in a model of biological tissues, Soft Matter 16, 5942 (2020).
  49. D. Hexner and D. Levine, Hyperuniformity and critical absorbing states, Phys. Rev. Lett. 114, 110602 (2015).
  50. D. Hexner, A. J. Liu, and S. R. Nagel, Two diverging length scales in the structure of jammed packings, Phys. Rev. Lett. 121, 115501 (2018).
  51. D. Hexner, P. M. Chaikin, and D. Levine, Enhanced hyperuniformity from random reorganization, Proc. Natl. Acad. Sci. USA 114, 4294 (2017).
  52. S. Wilken, R. E. Guerra, D. J. Pine, and P. M. Chaikin, Hyperuniform structures formed by shearing colloidal suspensions, Phys. Rev. Lett. 125, 148001 (2020).
  53. Y. Zheng, A. D. S. Parmar, and M. P. Ciamarra, Hidden order beyond hyperuniformity in critical absorbing states, Phys. Rev. Lett. 126, 118003 (2021).
  54. S. Torquato, J. Kim, and M. A. Klatt, Local number fluctuations in hyperuniform and nonhyperuniform Systems: Higher-order moments and distribution functions, Phys. Rev. X 11, 021028 (2021).
  55. See the SM for estimates of γ(R) and κ(R) at R=l1, R=ξh, and R=102 for various AX.
  56. H. Ikeda, Correlated noise and critical dimensions, Phys. Rev. E 108, 064119 (2023).
  57. H. Ikeda and Y. Kuroda, Continuous symmetry breaking of low-dimensional systems driven by inhomogeneous oscillatory driving forces, Phys. Rev. E 110, 024140 (2024).
  58. A. Tiribocchi, R. Wittkowski, D. Marenduzzo, and M. E. Cates, Active model H: Scalar active matter in a momentum-conserving fluid, Phys. Rev. Lett. 115, 188302 (2015).
  59. J. Stenhammar, D. Marenduzzo, R. J. Allen, and M. E. Cates, Phase behaviour of active Brownian particles: The role of dimensionality, Soft Matter 10, 1489 (2014).

Outline

Information

Phys. Rev. Research 6, L032056– Published 6 September, 2024
  • Received 5 October 2023
  • Accepted 27 May 2024
Crossmark - Check for updates button
Creative Commons Logo

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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation