Chaotic Dynamics of Superconductor Vortices in the Plastic Phase

We present numerical simulation results of driven vortex lattices in the presence of random disorder at zero temperature. We show that the plastic dynamics is readily understood in the framework of chaos theory. Intermittency “routes to chaos” have been clearly identified, and positive Lyapunov exponents and broadband noise, both characteristic of chaos, are found to coincide with the differential resistance peak. Furthermore, the fractal dimension of the strange attractor reveals that the chaotic dynamics of vortices is low dimensional.

Figure 1

Properties of the transition region from phase II to phase III in the weak pinning case. It clearly displays the type I intermittency route to chaos characteristics. (a) Part of the time evolution of the longitudinal velocity $V_x^{\mathrm{cm}}(t)$ obtained for $F^L=1.5221\times {10}^{-4}$. One sees laminar (i.e., periodic) phases interrupted by chaotic bursts of large velocity fluctuations. (b) Distribution of the laminar phase durations of $V_x^{\mathrm{cm}}(t)$ measured for $F^L=1.5221\times {10}^{-4}$. (c) Evolution of ${\tau }_{\max }$ when varying the applied force $F^L$ from the intermittency threshold force $F_t^L$. A clear power law is observed as shown with the line of slope $-1/2$.

Figure 2

Evolution of the maximal Lyapunov exponent $\lambda$ with the Lorentz force in phase III. Each point is the average of 20 couples of initial conditions, and the error bars are the standard deviation. The inset displays the time evolution of the distance $d(t)$ between two initial neighboring trajectories in the phase space for $F^L=0.0029$ in the strong pinning case. The exponential divergence (positive slope $\lambda$) characteristic of chaos is obvious for $t<{\tau }_{\mathrm{chaos}}$. For time scales larger than ${\tau }_{\mathrm{chaos}}$, diffusive motion is observed as already shown in Ref. 6.

Figure 3

Evolution of the strange attractor fractal dimension (computed with the correlation dimension $\nu$) with the Lorentz force in phase III. The inset displays the differential resistance curve (solid circles) and the low frequency longitudinal $B_x$ (open circles) and transverse $B_y$ (triangles) noises. Dotted lines separate phases II, III, and IV.