Self-organized, noise-free escape of a coupled nonlinear oscillator chain

We consider the self-organized escape of a chain of harmonically coupled units from a metastable state over a cubic potential barrier. The underlying dynamics is conservative and purely deterministic. The supply of a sufficient total energy transforms the chain into the nonlinear regime from which an initially, nearly uniform lattice configuration becomes unstable, yielding a redistribution with a strong localization of energy. A spontaneously emerging localized mode grows into the critical nucleus. Upon passing this transition state, the nonlinear chain performs a collective, deterministic escape event. Surprisingly, we find that such noise-free, collective nonlinear barrier crossing events yield a drastically diminished average escape time as compared to the one that is assisted by continuously impacting thermal noise. This beneficial enhancement of the rate of escape for the chain typically occurs whenever the ratio between the average energy supplied per unit in the chain and the potential barrier energy assumes small values. Copyright c © EPLA, 2007 Ever since the benchmark work by Kramers (for a comprehensive review see ref. [1]), there is continued and growing interest in the dynamics of escape processes of single particles, of coupled degrees of freedom or of small chains of coupled objects out of metastable states. It is realized by the passage of the considered objects over an energetic barrier which separates the local potential minimum from a neighboring attracting domain. A common situation in statistical physics is that of a stochastic escape for which the total energy remains a constant on average only. The later circumstance assumes the existence of a thermal bath, causing dissipation and local energy fluctuations. Thus, in this situation the escape necessitates the creation of an optimal fluctuation triggering the escape [1]. Put differently, when such an optimal fluctuation is transferred to the chain it provides sufficient energy to the chain to statistically overcome the energetic bottleneck. Characteristic time-scales of these processes are determined by the calculation of corresponding rates of escape out of the corresponding domain of attraction. Consequently, many generalizations of Kramers escape theory [1] in overand underdamped versions have been widely exploited. First extensions to multi-dimensional systems date back to the late ’60s [2]. Nowadays, this method is commonly utilized in biophysical contexts and for a great many applications occurring in physics and chemistry [3–10]. The objective of this letter is to elaborate on a different scenario of the possible exit from a metastable domain of attraction; the main mechanism is based on the assistance of a strongly nonlinear deterministic dynamics. The model we shall investigate is a purely deterministic dynamics of a bi-linearly coupled chain of nonlinear oscillators. Thus, no additional coupling to a thermal bath assists the escape. This set-up thus implies a vanishing dissipation. We consider macroscopic discrete, coupled nonlinear oscillator chains with up to 1000 links, as these may appear as realistic models in neuroscience, in various biophysical contexts or also in networks of coupled superconductors, e.g. see refs. [11–14]. An efficient deterministic escape that is driven in the absence of noise is particularly important when dealing with low temperatures for which the activated escape becomes far too slow, or also for situations with many coupled nonlinear units in the presence of non-thermal intrinsic noise that scales inversely with the square root of the system size. If the chain is brought into the nonlinear regime it may exhibit a spontaneous energy localization. This is due to a modulational instability [15]