Noise induced patterning in periodic systems with conserved dynamics (original) (raw)

Noise-Induced Phase Space Transport in Time-Periodic Hamiltonian Systems

Orbits in a three-dimensional potential subjected to periodic driving, V(x^i,t)=[1+m_0 sin(omega t) V_0(x^i), divide naturally into two types, regular and chaotic, between which transitions are seemingly impossible. The chaotic orbits divide in turn into two types, apparently separated by entropy barriers, namely `sticky' orbit segments, which are `locked' to the driving frequency and exhibit little systematic energy diffusion, and `wildly' chaotic segments, which are not so locked and can exhibit significant energy diffusion. Attention focuses on how the relative abundance of these different orbit types and the transition rate between sticky and wildly chaotic orbits depends on amplitude m_0, and on the extent to which these quantities can be altered by weak friction and/or noise and by pseudo-random variations in the driving frequency, idealized as an Ornstein-Uhlenbeck process with (in general) nonzero autocorrelation time t_c. When, in the absence of perturbations, t...