Exploring the Kibble–zurek Mechanism in a Secondary Bifurcation

Abstract

We present new experimental results on the quenching dynamics of an extended thermo-convective system (a network array of approximately 100 convective oscillators) going through a secondary subcritical bifurcation. We characterize a dynamical phase transition through the nature of the domain walls (1D-fronts) that connect the basic multicellular pattern with the new oscillating one. Two different mechanisms of the relaxing dynamics at the threshold are characterized depending on the crossing rate µ = dε dt ε=0(where ε is the control parameter) of the quenched transition. From the analysis of fronts, we show that these mechanisms follow different correlation length scales ξ ∼ µ −σ . Below a critical value µc a slow response dynamics yields a spatiotemporal coherent front with weak coupling between oscillators. Above µc, for rapid quenches, defects are trapped at the front with a strong coupling between oscillators, similarly to the Kibble-Zurek mechanism in quenched phase transitions. These defects, which are pinned to the fronts, yield a strong decay of the correlation length.

Frozen dynamics and synchronization through a secondary symmetry-breaking bifurcation

“…Coexistence between these patterns in the case of ST/ALT + TW and TW + ALT below a Co-2 point and a detailed explanation of the stability diagram structure have been previously reported (see Ref. [13], and references therein). In accordance with that work, it should be noticed from Fig.…”

“…[27,28]. In this scenario, the present study represents a further step from the previous work in quenched convection [13,[29][30][31][32].…”

“…Previous experiments on the KZ mechanism for a weak subcritical regime, which correspond to a depth of the fluid layer of d = 7.5 mm, are reported in Ref. [13]. The quenched dynamics is inferred from the homogeneity of the transition 1D front, and thus, the correlation length of the 1D front accounts for the phenomenon of defect appearance at different crossing rates.…”

“…As the speed at which the threshold [ = 0 in Fig. 1(b)] is crossed increases, the system bifurcates towards the ALT pattern as a secondary doubling wavelength bifurcation with the presence of a homogeneous synchronization 1D front except for the trapped defects [13]. In Fig.…”

“…Precedents on synchronization are found in the pioneering work by Winfree [1] and Kuramoto [2] and in the research on collective behavior in life sciences like neurology [3], ecology [4], and networks [5][6][7][8][9][10]. However, joint experimental [11][12][13][14][15] and theoretical [16][17][18] efforts have been scarce, and more research must be devoted to the understanding of synchronization processes in complex systems from the networks approach.…”