Energy diffusion and prethermalization in chaotic billiards under rapid periodic driving.

We study the energy dynamics of a particle in a billiard subject to a rapid periodic drive. In the regime of large driving frequencies ω, we find that the particle's energy evolves diffusively, which suggests that the particle's energy distribution η(E,t) satisfies a Fokker-Planck equation. We calculate the rates of energy absorption and diffusion associated with this equation, finding that these rates are proportional to ω^{-2} for large ω. Our analysis suggests three phases of energy evolution: Prethermalization on short timescales, then slow energy absorption in accordance with the Fokker-Planck equation, and finally a breakdown of the rapid driving assumption for large energies and high particle speeds. We also present numerical simulations of the evolution of a rapidly driven billiard particle, which corroborate our theoretical results.

Lock-and-key dimerization in dense Brownian systems of hard annular sector particles.

We develop a translational-rotational cage model that describes the behavior of dense two-dimensional (2D) Brownian systems of hard annular sector particles (ASPs), resembling C shapes. At high particle densities, pairs of ASPs can form mutually interdigitating lock-and-key dimers. This cage model considers either one or two mobile central ASPs which can translate and rotate within a static cage of surrounding ASPs that mimics the system's average local structure and density. By comparing with recent measurements made on dispersions of microscale lithographic ASPs [P. Y. Wang and T. G. Mason, J. Am. Chem. Soc. 137, 15308 (2015)JACSAT0002-786310.1021/jacs.5b10549], we show that mobile two-particle predictions of the probability of dimerization P_{dimer}, equilibrium constant K, and 2D osmotic pressure Π_{2D} as a function of the particle area fraction ϕ_{A} correspond closely to these experiments. By contrast, predictions based on only a single mobile particle do not agree well with either the two-particle predictions or the experimental data. Thus, we show that collective entropy can play an essential role in the behavior of dense Brownian systems composed of nontrivial hard shapes, such as ASPs.