Noisy zigzag transition, fluctuations, and thermal bifurcation threshold

International audienceWe study the zigzag transition in a system of particles with screened electrostatic interaction, submitted to a thermal noise. At finite temperature, this configurational phase transition is an example of noisy supercritical pitchfork bifurcation. The measurements of transverse fluctuations allow a complete description of the bifurcation region, which takes place between the deterministic threshold and a thermal threshold beyond which thermal fluctuations do not allow the system to flip between the symmetric zigzag configurations. We show that a divergence of the saturation time for the transverse fluctuations allows a precise and unambiguous definition of this thermal threshold. Its evolution with the temperature is shown to be in good agreement with theoretical predictions from noisy bifurcation theory. Many systems exhibit a topological transition as soon as a parameter β, which controls this transition, reaches a threshold β ZZ. An example of such transitions is the " zigzag bifurcation, " which involves a quasi-one-dimensional (1D) chain of interacting particles confined in a narrow channel that forbids any particle crossing [1]. At T = 0 K and for an infinite system, the particles remain aligned until the transverse component of the interparticle forces exceeds the transverse confinement, which may be expressed as β > β ZZ if β is the transverse stiffness [see Fig. 1(a)]. The bifurcation occurs when these two contributions are equal, β = β ZZ. Beyond that, for β β ZZ to a finite value y(β) = ±(β ZZ − β) 1/2 as the difference β ZZ − β increases. This bifurcation is purely mechanical. The zigzag threshold β ZZ is called the deterministic threshold and noted β ZZ (0) ≡ β ZZ (T = 0). When the confined particles interact with a thermal bath, the topological properties are no longer sufficient to describe the states of the system. Although the equilibrium configurations are independent of the temperature, the thermal fluctuations directly modify the bifurcation scheme. Far from the threshold, when the system is strongly stable, these fluctuations do not modify the stability of the system, but they have a large influence near the bifurcation since the system is then very sensitive to any small perturbation. In particular, just beyond the deterministic bifurcation threshold [β 0 K, β ZZ (T) is not so accurate since the y(β) curve is broadened by the thermal fluctuations which smooth out th