Hysteretic and intermittent regimes in the subcritical bifurcation of a quasi-one-dimensional system of interacting particles.

In this article, we study the effects of a white gaussian additive thermal noise on a subcritical pitchfork bifurcation. We consider a quasi-1D system of particles that are transversally confined, with short range (non Coulombic) interactions and periodic boundary conditions in the longitudinal direction. In such systems, there is a structural transition from a linear order to a staggered raw, called the zigzag transition. There is a finite range of transverse confinement stiffnesses for which the stable configuration at zero temperature is a localized zigzag pattern surrounded by aligned particles, which evidences the subcriticality of the bifurcation. We show that these configurations remains stable for a wide temperature range. At zero temperature, the transition between a straight line and such localized zigzag patterns is hysteretic. We have studied the influence of the thermal noise on the hysteresis loop. Its description is more difficult than at $T=0$~K since thermally activated jumps between the two configurations always occur and the system can never stay forever in a unique metastable state. Two different regimes have to be considered according to the temperature value with respect to a critical temperature $T_c(\tau_{obs})$ that depends on the observation time $\tau_{obs}$. An hysteresis loop is still observed at low temperature, with a width that decreases as the temperature increases toward $T_c(\tau_{obs})$. In contrast for $T>T_c(\tau_{obs})$ the memory of the initial condition is lost by stochastic jumps between the configurations. The study of the mean residence times in each configurations gives a unique opportunity to precisely determine the barrier height that separates the two configurations, without knowing the complete energy landscape of this many-body system. We also show how to reconstruct the hysteresis loop which would exist at $T=0$~K from high temperature simulations.