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Particle traps and stationary currents captured by an active 1D model

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  • Cirillo, Emilio N.M.
  • Colangeli, Matteo
  • Di Francesco, Antonio
  • Kröger, Martin
  • Rondoni, Lamberto

Abstract

We investigate the onset of a non-equilibrium phase transition in a one-dimensional ring, constituted by two urns connected by two strands, called active and passive channels. A set of N particles move inside the ring with constant individual speeds; collisions against the channel entries produce reflections with certain probabilities, that differ between active and passive channels. The microscopic dynamics differs from a classical 1D billiard owing to the presence of an interaction mechanism acting inside the active channel, which potentially reverses velocities of its particles. We outline a general theory for the feedback-controlled system which describes quantitatively the phase diagram of the model, based on a mixing property, that is analytically predicted and numerically verified. The probability distributions we define and evolve in time are 1D projections of uniform distributions on d-dimensional spherical surfaces, with d≥1 and d=∞. Consequently results that apply to higher dimensional systems are recovered.

Suggested Citation

  • Cirillo, Emilio N.M. & Colangeli, Matteo & Di Francesco, Antonio & Kröger, Martin & Rondoni, Lamberto, 2024. "Particle traps and stationary currents captured by an active 1D model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 642(C).
  • Handle: RePEc:eee:phsmap:v:642:y:2024:i:c:s0378437124002723
    DOI: 10.1016/j.physa.2024.129763
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    References listed on IDEAS

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    4. Livorati, André L.P. & Loskutov, Alexander & Leonel, Edson D., 2012. "A peculiar Maxwell’s Demon observed in a time-dependent stadium-like billiard," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(20), pages 4756-4762.
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