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Modeling chiral active particles: from circular motion to odd interactions

Lorenzo Caprini, Alessandro Petrini, Umberto Marini Bettolo Marconi

TL;DR

The paper addresses how chiral active particles, which exhibit circular trajectories, generate non-conservative odd (transverse) interactions that break mirror symmetry. It develops microscopic models spanning circular self-propelled motion, coarse-grained transverse forces, and granular spinner-based odd interactions, showing how inertia and chirality cooperate to produce a novel BIO (bubbles induced by odd interactions) phase—an inhomogeneous state with particle-free bubbles and edge currents. The work derives both numerical phase diagrams and analytical insights, including an instability condition $m C_0 = \beta_1 \tau_I^2 C_1^2$ and a critical scaling $\omega_c^2 \sim m\epsilon/(\tau_I^2 \sigma^2)$, revealing how increasing inertia lowers the threshold chirality for BIO. Spatial velocity correlations show a finite-$q^*$ signature and oscillatory real-space behavior, supporting a non-equilibrium phase transition separate from classical MIPS. Overall, the BIO phase uncovers a new class of collective behavior in chiral active matter driven by odd interactions, with open questions about a full hydrodynamic or kinetic description and potential experimental realizations.

Abstract

In this paper, we discuss microscopic models for chiral active particles, i.e., rotating active units that exhibit circular or spinning motion. While non-chiral active particles are typically governed by self-propulsion and conservative interactions, the rotating motion of chiral particles generates additional non-conservative forces that cannot be derived from a potential. These manifest as effective transverse forces, acting perpendicular to the line connecting the centres of two interacting particles, and are referred to as odd interactions, because they break the mirror symmetry of the system. Here, we demonstrate that odd interactions arise from a limiting case of a well-established model describing spinning granular objects. In addition, we show that these models for chiral active objects give rise to a novel collective phenomenon that emerges uniquely from transverse forces and, hence, chirality. Specifically, the system undergoes a transition from a homogeneous phase to an inhomogeneous one characterised by regions depleted of particles, referred to as bubbles. This collective behaviour, termed BIO (bubbles induced by odd interactions), is a general emergent phenomenon arising from chirality and odd interactions. In this work, we review theoretical approaches to this problem, including a scaling argument and predictions for spatial velocity correlations that account for the BIO phase. Finally, we outline perspectives and open challenges concerning this collective phenomenon.

Modeling chiral active particles: from circular motion to odd interactions

TL;DR

The paper addresses how chiral active particles, which exhibit circular trajectories, generate non-conservative odd (transverse) interactions that break mirror symmetry. It develops microscopic models spanning circular self-propelled motion, coarse-grained transverse forces, and granular spinner-based odd interactions, showing how inertia and chirality cooperate to produce a novel BIO (bubbles induced by odd interactions) phase—an inhomogeneous state with particle-free bubbles and edge currents. The work derives both numerical phase diagrams and analytical insights, including an instability condition and a critical scaling , revealing how increasing inertia lowers the threshold chirality for BIO. Spatial velocity correlations show a finite- signature and oscillatory real-space behavior, supporting a non-equilibrium phase transition separate from classical MIPS. Overall, the BIO phase uncovers a new class of collective behavior in chiral active matter driven by odd interactions, with open questions about a full hydrodynamic or kinetic description and potential experimental realizations.

Abstract

In this paper, we discuss microscopic models for chiral active particles, i.e., rotating active units that exhibit circular or spinning motion. While non-chiral active particles are typically governed by self-propulsion and conservative interactions, the rotating motion of chiral particles generates additional non-conservative forces that cannot be derived from a potential. These manifest as effective transverse forces, acting perpendicular to the line connecting the centres of two interacting particles, and are referred to as odd interactions, because they break the mirror symmetry of the system. Here, we demonstrate that odd interactions arise from a limiting case of a well-established model describing spinning granular objects. In addition, we show that these models for chiral active objects give rise to a novel collective phenomenon that emerges uniquely from transverse forces and, hence, chirality. Specifically, the system undergoes a transition from a homogeneous phase to an inhomogeneous one characterised by regions depleted of particles, referred to as bubbles. This collective behaviour, termed BIO (bubbles induced by odd interactions), is a general emergent phenomenon arising from chirality and odd interactions. In this work, we review theoretical approaches to this problem, including a scaling argument and predictions for spatial velocity correlations that account for the BIO phase. Finally, we outline perspectives and open challenges concerning this collective phenomenon.
Paper Structure (9 sections, 20 equations, 3 figures)

This paper contains 9 sections, 20 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Microscopic models for chiral active particles
  3. Circular self-propelled motion
  4. Coarse-grained description for chirality-induced transverse forces
  5. Odd interactions emerging in models for granular spinners
  6. A chirality-induced collective effect: bubbles induced by odd interactions -- the BIO phase
  7. The BIO phase
  8. Conclusions and perspectives
  9. Acknowledgement

Figures (3)

  • Figure 1: (a) Illustration of a collision between two chiral particles, governed by pure repulsive forces, $\mathbf{F}_i$ and odd interactions $\mathbf{F}^{odd}_i$. The repulsive forces are directed tangentially along with the direction connecting the centers of the two particles, while odd interactions are directed normally compared to this direction. Panels (a) is adapted with permission from Ref. caprini2025bubble; copyright (2025) AIP Publishing. (b) Colloidal particles driven to spin by external magnetic fields. Panel (b) is adapted with permission from Ref. yan2015rotating. (c) Rayleigh--Bénard convection cells organized in a hexagonal pattern, which show odd elasticity when the system is put under rotation. Panel adapted from Ref. an2010int. (d) Left-handed and right-handed vibrobots manufactured by 3D printing. Panel (d) is adapted with permission from Ref. scholz2021surfactants.
  • Figure 2: BIO phase: Bubbles induced by odd interactions. (a)-(b) Snapshot configurations showing the homogeneous and BIO (bubbles induced by odd interactions) phases. The scale bars referring to both panels denote 10 $\sigma$ where $\sigma$ is the particle diameter. (c) Phase diagram in the plane of chirality $\omega/\epsilon$, i.e. the strength of odd interactions, and reduced inertia, $\tau_I/\tilde{t}$ (with $\tilde{t}=\sigma \sqrt{m/\epsilon}$), showing homogeneous (grey points) and BIO phases (yellow points). The dashed black line marks the scaling $\omega\sim1/\tau_I$ for the transition line from the two phases, while the two stars correspond to the two configurations in panels (a) and (b). Panels (a), (b), and (c) are adapted with permission from Ref. caprini2025bubble; copyright (2025) AIP Publishing.
  • Figure 3: Edge currents and centrifugal forces generated by odd interactions. (a) Snapshot configuration showing a BIO phase (bubbles induced by odd interactions) where black arrows denote the particle velocities and points represent particles. In addition, a zoom of panel (a) is reported with an additional violet arrow showing edge currents (counterclockwise rotation). (b) illustration of the mechanism responsible for the bubble stability showing the competition between the net force, due to repulsive interactions, and the centrifugal force generated by odd interactions. Panels (a) and (b) are adapted with permission from Ref. caprini2025bubble; copyright (2025) AIP Publishing.