1/f noise in a thin stochastic layer described by the discrete nonlinear Schrödinger equation.
We investigate the nonlinear dynamics in a trimer, described by the one-dimensional discrete nonlinear Schrödinger equation, with periodic boundary conditions in the presence of a single on-site defect. We make use of numerical continuation to study different families of stationary and periodic solutions in this Hamiltonian system. Taking into account a suitable Poincaré section, we are able to study the dynamics of a generic thin stochastic layer in this conservative system. Our results strongly suggest that intermittency, on the one hand, and transport between two almost invariant sets, on the other hand, are relevant features of the chaotic dynamics. This behavior arises as a result of the formation of the above mentioned stochastic layer connecting two hyperbolic fixed points of the Poincaré return map. We find that the transit times, the time intervals to traverse some suitable sets in phase space, generate 1/f noise. Its origin is explained in terms of a hopping mechanism in a suitable discrete state space of transit times. A qualitatively similar behavior is also found in the standard map, which shows the generic nature of this mechanism. As a physical application of our results, we consider a possible experiment in a ring of weakly coupled Bose-Einstein condensates (BECs) with attractive interactions, where intermittent bursts of the relative phase of two spatially symmetric BECs take place.
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IFUAP, Universidad Autónoma de Puebla, Apartado Postal J-48, Puebla, Puebla 72570, Mexico.
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