A Non-Equilibrium Defect-Unbinding Transition: Defect Trajectories and Loop Statistics

Details A Non-Equilibrium Defect-Unbinding Transition: Defect Trajectories and Loop Statistics A Non-Equilibrium Defect-Unbinding Transition: Defect Trajectories and Loop Statistics

2001-01-09

arxiv.org/abs/nlin/0101019v1

Nonlinear Sciences

Chaotic Dynamics

4 pages 5 figures

Scientific paper

10.1103/PhysRevLett.87.174502

In a Ginzburg-Landau model for parametrically driven waves a transition between a state of ordered and one of disordered spatio-temporal defect chaos is found. To characterize the two different chaotic states and to get insight into the break-down of the order, the trajectories of the defects are tracked in detail. Since the defects are always created and annihilated in pairs the trajectories form loops in space time. The probability distribution functions for the size of the loops and the number of defects involved in them undergo a transition from exponential decay in the ordered regime to a power-law decay in the disordered regime. These power laws are also found in a simple lattice model of randomly created defect pairs that diffuse and annihilate upon collision.

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