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Breakdown and Restoration of Hydrodynamics in Dipole-conserving Active Fluids

Anish Chaudhuri, Lokrshi Prawar Dadhichi, Arijit Haldar

Abstract

We present a general hydrodynamic theory for active fluids, capable of describing living matter, that conserve center of mass or dipole moment. Imposition of dipole or center-of-mass conservation has been reported to yield peculiar behavior: breaking Galilean invariance in classical systems and potentially enabling exotic immobile excitations in quantum settings. In passive fluids, dipole conservation has been shown to cause a breakdown of linear hydrodynamics in all experimentally relevant dimensions. We show that introducing activity changes this picture: it can either restore or break linear hydrodynamics depending on spatial dimensions. Using our formulation, we predict universal dynamical scaling exponents for single-component active fluids in $d=1,2,3$ dimensions and find agreement with microscopic lattice-field simulations. Strikingly, for $d\geq 2$, activity revives linear hydrodynamics, while for $d<2$ it leads to a breakdown; both cases flow to previously unexplored universality classes. Our results suggest that dipole-conserving active fluids are far more experimentally accessible than their passive counterparts.

Breakdown and Restoration of Hydrodynamics in Dipole-conserving Active Fluids

Abstract

We present a general hydrodynamic theory for active fluids, capable of describing living matter, that conserve center of mass or dipole moment. Imposition of dipole or center-of-mass conservation has been reported to yield peculiar behavior: breaking Galilean invariance in classical systems and potentially enabling exotic immobile excitations in quantum settings. In passive fluids, dipole conservation has been shown to cause a breakdown of linear hydrodynamics in all experimentally relevant dimensions. We show that introducing activity changes this picture: it can either restore or break linear hydrodynamics depending on spatial dimensions. Using our formulation, we predict universal dynamical scaling exponents for single-component active fluids in dimensions and find agreement with microscopic lattice-field simulations. Strikingly, for , activity revives linear hydrodynamics, while for it leads to a breakdown; both cases flow to previously unexplored universality classes. Our results suggest that dipole-conserving active fluids are far more experimentally accessible than their passive counterparts.
Paper Structure (14 sections, 86 equations, 2 figures, 2 tables)

This paper contains 14 sections, 86 equations, 2 figures, 2 tables.

Table of Contents

  1. Continuity equation
  2. Free energy form
  3. Identification of forces and fluxes
  4. Hydrodynamic equations of motion
  5. The linear theory
  6. Dispersion relations
  7. Exceptional point
  8. Correlator
  9. Estimation of dynamical exponent in $d < d_c$
  10. Additional details of microscopic lattice model
  11. Continuum limit of lattice model
  12. Breakdown of Fluctuation-Dissipation Theorem (FDT)
  13. Quantitative analysis of collapse
  14. Extracting dynamical exponent $z$ from feature tracking

Figures (2)

  • Figure 1: Panels (a--c) show log–log plots of the momentum correlator $C_\pi(k_x,t)= \langle p^{(x)}_{k_x, k_\perp}(t)p^{(x)}_{-k_x, -k_\perp}(t) \rangle|_{k_\perp=0}$ versus wavenumber $k_x$ at different times $t$ in dimensions $d=3,2,1$, respectively. Panels (d--f) show the scaled forms $C_\pi(k_x t^{1/z}) t^{-\alpha}$, corresponding to panels (a--c), and their collapse onto a universal curve. Insets display the respective optimal $\alpha$ and $z$ values, obtained by minimizing the collapse error in the $(\alpha, z^{-1})$ plane (see app. \ref{['app:collapse_err']}). Independent confirmation of optimized $z$ values is obtained by tracking the time evolution of the marked features ($\hbox{origin=c]{45}{$\blacksquare$}},~\bm{\triangledown},~\circ,~\bullet$).(See app. \ref{['app:tvsk']} for details.)
  • Figure 2: The inverse characteristic wavenumber $1/k^*$ versus $t$ plotted in log-log scale. Using a linear fit, the dynamical exponent $z$, for $d=1, 2$, and $3$ dimensions, can be found from the inverse of the slope obtained from the fit.