Kibble-Zurek mechanism in a pattern forming secondary bifurcation

Abstract

We present new experimental results on the quenching dynamics of an extended thermo-convective system (a network array of 100 c onvective oscil- lators) through a secondary bifurcation. The topology of th e new coherent struc- tures which are fronts (domain walls), when this secondary bi furcation is crossed upwards from a basic stationary multicellular pattern towar ds a propagative pat- tern, allows us to characterize a freezing dynamics related t o the Kibble-Zurek mechanism (KZM). This mechanism defines a correlation length ξ ∼

σ when the threshold has been crossed at a quench rate

= dǫ dt | ǫ =0 sufficiently large to freeze almost instantaneously the phase transition front. This stu dy concerns several sequences of quenches where convective oscillators become d ifferently correlated depending on

. Spatio-temporal correlation analysis will allow us to deter mine the behavior of the KZM from the front dynamics. The novelty of these results is that the front dynamics is expected to show the freezing-out dy namics beyond the threshold, and therefore it will provide the healing length of the system depending on the strength of the quench rate. Furthermore, in our system the effect of res- onant nonlinearities pins the front and diminishes its fluctu ations as we increase the quench rate.