Breaking chirality in nonequilibrium systems

Abstract

At equilibrium, Bloch walls are chiral interfaces between domains with different magnetization. Far from equilibrium, a set of forced oscillators can exhibit walls between states with different phases. In this Letter, we show that when these walls become chiral, they move with a velocity simply related to their chirality. This surprising behavior is a straightforward consequence of nonvariational effects, which are typical of nonequilibrium systems.PACS numbers: 47.10.+g, 05.45.+b, 47.20.Ky Domain walls exhibit phase transitions, where Ising walls become Bloch walls,' and which have been related to spontaneous breaking of chirality, 2,3 in the frame of an anisotropic X-Y model. In this Letter, we investigate the nonequilibrium analog of these transitions. Namely, we consider the parametric forcing of an assembly of self-oscillators. In such a system, "phase anisotropy," induced by the forcing, provides a natural counterpart to crystalline anisotropy which allows the existence of walls. We show that spontaneous breaking of chirality is accompanied by the motion of chiral interfaces. A simple analysis allows us to describe this behavior. Since this motion is due to nonvariational effects, it is generic to nonequilibrium systems. The occurrence of such effects has been recently emphasized, 4 " 8 and here is another manifestation of these phenomena. In conclusion, we suggest an experiment where these phenomena are likely to be observed.We consider a one-dimensional system which undergoes a spatially homogeneous Hopf bifurcation, 9 with temporal frequency coo. Such a system can be seen as a continuous assembly of oscillators, which auto-oscillate above the Hopf bifurcation threshold. Now, we parametrically force this system at twice its natural frequency too. Let A be the complex order parameter which measures the amplitude of oscillations. It is assumed to vary slowly in space and time and obeys the following Ginzburg-Landau equation:where p measures the distance from the oscillatory instability threshold, v is the detuning parameter, V stands for d/dx, and y > 0 is the forcing amplitude.When the real parameters v, a, and j3 vanish, Eq. (1) can be cast into a variational form:bt 8Awhere 7 -J {-p CY 2 + v 2 ) + \vx\ 2 + |vr| 2 + HX 2 +Y 2 ) 2 -r (X 2 -Y 2 )}dx and A =X + iY. The quantity J turns out to be the free energy of the X-Y model in the presence of weak anisotropy whose amplitude is controlled by 7. In this limit, Eq.(1) exhibits spontaneous breaking of chirality. 2 Namely, Eq. (2) possesses stationary kinklike solutions 1,10 which connect stable homogeneous solutions (X=± VAI + 7, F=0). They read X I = ±Jp + ytanh{[{(p + y)] {/2 x}, r,=0, A-fl = ±v^T7tanh(V27x), Y B -±

Fronts and patterns in a spatially forced CDIMA reaction

“…These front bifurcations are the spatial counterparts of the so-called nonequilibrium Ising-Bloch (NIB) bifurcation in temporally forced oscillatory systems. [23][24][25][26] We refer to fronts that shift the phase discontinuously and continuously as Ising and Bloch fronts, respectively.…”

Bloch Brane

“…The chiral feature of Bloch walls was first explored in Ref. [19]; other recent investigations on Bloch walls in parametrically driven systems may be found in [20], and in references therein.…”

Spontaneous motion of localized structures and localized patterns induced by delayed feedback

“…Transverse optical structures can be either stationary or not. The motion can be induced by the vorticity [28,29], by finite relaxation rates [30][31][32], phase gradient [33], so-called Ising-Bloch transition [34][35][36], by walk-off or convection or by the symmetry breaking due to off-axis feedback [37][38][39][40][41], or even by resonator detuning [42]. This subject is relatively well understood (see overviews on that issue [43][44][45][46][47][48][49][50][51][52][53][54]).…”