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Dynamical patterns and nonreciprocal effective interactions in an active-passive mixture through exact hydrodynamic

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Dynamical patterns in nonequilibrium systems emerge from nonreciprocal interactions. This study introduces a tractable model revealing novel phase diagrams and steady states in active-passive particle mixtures.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Soft Matter Physics

Background:

  • Dynamical pattern formation is a key feature of nonequilibrium physical systems.
  • Nonreciprocal interactions, violating Newton's third law, are known to drive these patterns.
  • Analyzing these phenomena presents significant theoretical challenges.

Purpose of the Study:

  • To introduce a mathematically tractable model of active and passive particles.
  • To derive and analyze the hydrodynamic equations governing their collective behavior.
  • To explore the resulting phase diagram and emergent dynamical steady states.

Main Methods:

  • Development of a model mixture of active (self-propelled) and passive (diffusive) particles.
  • Exact derivation of hydrodynamic equations for particle densities using advanced analytical techniques.
  • Linear stability analysis of homogeneous states and investigation of phase coexistence.
  • Analysis of dynamical steady states in the thermodynamic limit.

Main Results:

  • Effective nonreciprocal couplings between active and passive species were identified.
  • A novel phase diagram was revealed, featuring a spinodal protruding through the binodal.
  • Dynamical steady states were shown to emerge, with sharp interfaces capable of traveling at finite velocities.
  • Traveling phase-separated states were demonstrated to be forbidden.

Conclusions:

  • The model provides a tractable framework for studying nonequilibrium phenomena driven by nonreciprocity.
  • It offers precise insights into phase separation and dynamical steady states in active-passive mixtures.
  • The mathematical tractability allows for conclusions beyond those from numerical simulations or complex field theories.