Statistical mechanics of phototactic robots
I will introduce a mathematical model of this experiment and study its properties in a certain limit, in which the dynamics simplifies to allow an explicit calculation of the stationary state. It turns out that the properties of the model depend in a sensitive way on the amount of the delay with which robots react to the light intensity. I will show that this delay can be meaningfully made negative, which means that the robots can be programmed to try to predict the future. For a certain negative value of the delay, the model undergoes a dynamical phase transition and its properties change qualitatively. This is in excellent agreement with the experimental results. I will discuss possible applications of this effect and, if time permits, I will mention several related models and projected experiments. The work I will describe was done jointly with Giovanni Volpe, Austin McDaniel and Mite Mijalkov.