Dynamically Emergent Correlations

Abstract

In this perspective article, we discuss the scenario of dynamically emergent correlation (DEC) arising in classical and quantum noninteracting systems when they are subjected to a common fluctuating stochastic environment. The key property of such systems is that the strong correlations between different particles emerge from the dynamics and not from built-in interactions. In many cases, these strong correlations persist even at long times in the stationary state. Computing observables explicitly for such strongly correlated states in general is very hard. Remarkably, the stationary states in several models of DEC exhibit an interesting analytical structure that allows to compute physical observables, despite being strongly correlated. Recent experiments on trapped colloidal particles have established that these DEC in the stationary state can in fact be measured. DEC is a rapidly emerging domain of strongly correlated out-of-equilibrium statistical physics, with both theoretical and experimental, as well as classical and quantum, components.

Figures (3)

• Figure 1: The left panel shows a schematic picture of an ideal gas of Brownian particles in a two-dimensional box of linear size $L(t)$ which switches between $L_1$ and $L_2$ in a noisy dichotomous (telegraphic) fashion, as shown in the right panel. The intervals between successive switches are drawn alternatively from exponential distributions $p_1(\tau) = r_1\, e^{-r_1 \tau}$ and $p_2(\tau) = r_2\,e^{-r_2 \tau}$ respectively. Here, $r_1$ and $r_2$ represent the Poissonian rates with which the box size switches from $L_1$ to $L_2$ and the reverse.
• Figure 2: Schematic trajectories of $N$ independent Brownian motions in one-dimension that start and reset simultaneously at the origin with rate $r$. This corresponds to the limiting case $L_1 \to 0$, $L_2 \to \infty$, $r_1 \to \infty$ and $r_2=r$ of Fig. \ref{['Fig_Intro']} in the $1d$ case. Here the $\tau_i$'s denote the intervals between successive resettings and are distributed independently, each drawn from $p(\tau) = r\,e^{-r \tau}.$
• Figure 3: The blue line shows the average density profile in Eq. (\ref{['eq:density']}).