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Deterministic active particles in the overactive limit
1Institute of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, 14476 Potsdam-Golm, Germany.
Chaos (Woodbury, N.Y.)
|November 7, 2023
Summary
This study examines deterministic active particles in external potentials. For identical particles, dynamics are conservative, but non-identical particles show shrinking phase volume, impacting Hamiltonian system formulations.
Area of Science:
- Physics
- Statistical Mechanics
- Dynamical Systems
Background:
- Deterministic active particles are crucial in modeling various physical phenomena.
- Understanding their dynamics in external potentials is key to predicting system behavior.
- Hamiltonian systems offer a framework for conservative dynamics, but their applicability to active particles requires investigation.
Purpose of the Study:
- To analyze two models of deterministic active particles in an external potential.
- To determine the conditions under which these models can be formulated as Hamiltonian systems.
- To investigate the impact of particle identity on the conservation of phase volume.
Main Methods:
- Formulation of active particle models in a fixed-speed limit.
- Analysis of system dynamics using Hamiltonian mechanics.
- Mathematical derivation of phase volume conservation for identical and non-identical particles.
Main Results:
- Both models approximate a Hamiltonian system when particle speed is fixed and the potential is time-independent.
- Identical particles exhibit conservative dynamics with conserved phase volume.
- Non-identical particles demonstrate shrinking phase volume, even with time-independent potentials.
Conclusions:
- The formulation of active particle systems as Hamiltonian systems is constrained by potential time-independence and particle identity.
- Particle interactions significantly influence phase volume conservation.
- The findings highlight fundamental differences in dynamics between identical and non-identical active particles.
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