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Review :�Anomalous transport of tracers in active bath

Ki-Won KIM

Department of Physics and Astronomy, Seoul National University

2nd DEC 2022 NEST meeting (on-line)

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Contents

  1. Introduction
  2. Review of the paper
  3. Conclusion

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Contents

  1. Introduction
  2. Review of the paper
  3. Conclusion

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What is active matter?

  • Nonequilibrium systems composed of self-driven units (active particles), each capable of converting ambient/stored energy into systematic motion.

Run-and-tumble particles (RTPs)

Persistent run punctuated by random tumble

Live active particle - E. Coli

[1] Howerd Berg’s lab

[2] Mehran Kardar’s lab

[1]

[2]

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Anomalous diffusion of tracers in active bath

  • Initial superdiffusion is observed for colloid particles (tracers) in active bath

[3] Wu and Libchaber. Phys Rev. Lett. 2000

[3]

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Anomalous diffusion of tracers in active bath

  • In adiabatic limit (the bath’s relaxation is much faster than the tracer’s response), the tracer’s dynamics is described by a general Langevin equation (overdamped) as,

 

Originate from interaction with active ptcls

Friction

Stochastic

force

White noise

 

 

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Anomalous diffusion of tracers in active bath

 

[4] D. T. N. Chen, A. W. C. Lau, L. A. Hough, M. F. Islam, M. Goulian, T. C. Lubensky, and A. G. Yodh. Phys Rev. Lett. 2007

[4]

  • This may lead to anomalous diffusion of tracers in active bath.

 

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Contents

  1. Introduction
  2. Review of the paper
  3. Conclusion

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System

  • A single tracer immersed in 1-D active bath of run-and-tumble particles(RTPs).
  • Mimicking the behavior of tracer in a narrow channel, RTPs are allowed to overtake each other and the tracers, and the tracers has soft repulsive potential.

 

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Result pre-summary

 

Asymmetric tracer

 

 

 

Symmetric tracer

 

 

 

 

 

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Result pre-summary

Negative active friction

Superdiffusion

 

 

Friction grows infinite

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Model

 

 

 

 

 

 

 

 

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Theory

 

  • In adiabatic limit,

 

= Friction

 

 

 

[5] Luca D'Alessio, Yariv Kafri and Anatoli Polkovnikov. J. Stat. Mech.: Theory Exp. (2016)

 

steady-state density of bath particles

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Theory

 

[5] Luca D'Alessio, Yariv Kafri and Anatoli Polkovnikov. J. Stat. Mech.: Theory Exp. (2016)

 

steady-state density of bath particles

 

 

 

 

 

 

Average force is zero at equilibrium

 

Thus, the relation reduces to FDT at equilibrium

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Theory

 

  • The master equation of RTPs become,

​

 

  • Then, the probability density of RTP follows,

​

 

  • The steady state solution of the equation is,

​

 

 

 

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Theory

Asymmetric tracer

 

 

 

 

 

 

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Theory

Asymmetric tracer

 

 

 

  • In the long-time limit, the dynamics of the RTPs are diffusive

​

 

 

 

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Theory

Asymmetric tracer

 

 

 

 

 

  • Since RTPs are non-interacting,

​

 

 

Force due to single RTP

 

 

 

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Theory

Asymmetric tracer

 

 

 

 

 

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Theory

Asymmetric tracer

 

 

 

 

 

 

 

 

 

 

 

 

 

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Theory

Asymmetric tracer

 

 

 

 

 

 

 

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Theory

Asymmetric tracer

 

 

 

Asymmetric tracer in the active bath shows superdiffusion.

 

 

 

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Theory

Symmetric tracer

 

 

 

 

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Theory

Symmetric tracer

 

 

 

 

 

 

 

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Theory

Symmetric tracer

 

 

 

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Theory

Symmetric tracer

 

 

 

 

 

 

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Theory

Symmetric tracer

 

 

 

 

 

 

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Theory

Symmetric tracer

 

 

 

 

 

 

 

 

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Theory

Symmetric tracer

 

 

 

 

 

 

 

 

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Theory

Symmetric tracer

 

 

 

 

 

 

 

 

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Theory

Symmetric tracer

 

 

  • This means a symmetric tracer in the active bath experiences normal diffusion in long-time scale.

 

 

 

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Contents

  1. Introduction
  2. Review of the paper
  3. Conclusion

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Conclusion

  • Authors investigated long-time dynamics of a passive tracer in a dilute active bath under the sole assumption of an adiabatic evolution.
  • Asymmetric tracers shows superdiffusion and also experience friction that grows with time when they are dragged at constant velocity.
  • Symmetric tracers shows normal diffusion in long-time but negative active friction is observed for small tracers.
  • Authors emphasize that the result stem from generic features of dry active particles and should thus hold generically.

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Thank you!