Brownian Molecules Formed by Delayed Harmonic Interactions

Abstract

A time-delayed response of individual living organisms to information exchanged within flocks or swarms leads to the emergence of complex collective behaviors. A recent experimental setup by (Khadka et al 2018 Nat. Commun. 9 3864), employing synthetic microswimmers, allows to emulate and study such behavior in a controlled way, in the lab. Motivated by these experiments, we study a system of N Brownian particles interacting via a retarded harmonic interaction. For $N\le 3$ , we characterize its collective behavior analytically, by solving the pertinent stochastic delay-differential equations, and for $N>3$ by Brownian dynamics simulations. The particles form molecule-like non-equilibrium structures which become unstable with increasing number of particles, delay time, and interaction strength. We evaluate the entropy and information fluxes maintaining these structures and, to quantitatively characterize their stability, develop an approximate time-dependent transition-state theory to characterize transitions between different isomers of the molecules. For completeness, we include a comprehensive discussion of the analytical solution procedure for systems of linear stochastic delay differential equations in finite dimension, and new results for covariance and time-correlation matrices.

36 pages, 26 figures, current version: further improvements and one correction

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Cited by in corpus (8)

• Irreversibility, heat and information flows induced by non-reciprocal interactions
• Spontaneous vortex formation by microswimmers with retarded attractions
• Finite-size scaling at the edge of disorder in a time-delay Vicsek model
• Signal propagation and linear response in the delay Vicsek model
• Reinforcement Learning of Artificial Microswimmers
• Equilibrium Stochastic Delay Processes
• Anti-persistent random walks in time-delayed systems
• Non-reciprocal hidden degrees of freedom: A unifying perspective on memory, feedback, and activity