Surmounting collectively oscillating bottlenecks

We study the collective escape dynamics of a chain of coupled, weakly damped nonlinear oscillators from a metastable state over a barrier when driven by a thermal heat bath in combination with a weak, globally acting periodic perturbation. Optimal parameter choices are identified that lead to a drastic enhancement of escape rates as compared to a pure noise-assisted situation. We elucidate the speed-up of escape in the driven Langevin dynamics by showing that the time-periodic external field in combination with the thermal fluctuations triggers an instability mechanism of the stationary homogeneous lattice state of the system. Perturbations of the latter provided by incoherent thermal fluctuations grow because of a parametric resonance, leading to the formation of spatially localized modes (LMs). Remarkably, the LMs persist in spite of continuously impacting thermal noise. The average escape time assumes a distinct minimum by either tuning the coupling strength and/or the driving frequency. This weak ac-driven assisted escape in turn implies a giant speed of the activation rate of such thermally driven coupled nonlinear oscillator chains. Copyright c © EPLA, 2008 Ever since the seminal work by Kramers (for a comprehensive review see ref. [1]) we witness a continual interest in the dynamics of escape processes of single particles, of coupled degrees of freedom or of chains of coupled objects out of metastable states. To accomplish the escape the considered objects must cross an energetic barrier, separating the local potential minimum from a neighboring attracting domain. From the perspective of statistical physics mainly the thermally activated escape, based on the permanent interaction of the considered system with a heat bath, has been studied [1]. The coupling to the heat bath causes dissipation and local energy fluctuations and the escape process is conditioned on the creation of a rare, optimal fluctuation which in turn triggers an escape. To put it differently, an optimal fluctuation transfers sufficient energy to the system so that the system is able to statistically surmount the energetic bottleneck associated with the transition state. Characteristic time-scales of such a process are determined by the inverse of corresponding rates of escape out of the domain of attraction. Within this topic, numerous extensions of Kramers escape theory and of first passage time problems have been widely investigated [1,2]. Early (a)E-mail: [email protected] generalizations to multi-dimensional systems date back to the late 1960s [3]. This method is by now well established and is commonly put to use in biophysical contexts and for great many other applications occurring in physics and chemistry and related areas [4–14]. In order that the system comprised of coupled units may pass through a transition state an activation energy Eact has to be concentrated in the corresponding critical localized mode (LM). In view of controlling the process of barrier crossing we intend to demonstrate that the formation of the critical LM can be distinctly accelerated via the application of a weak external ac-driving. By use of optimally oscillating barrier configurations it is feasible that a far faster escape can be promoted, leading to a drastic enhancement of the escape dynamics. Particularly at low temperatures, where the rate of thermal barrier crossing is exponentially suppressed, such a scenario can be very beneficial. Prior studies mainly dealt with the appearance of LMs in damped, driven deterministic nonlinear lattice systems [15–19]. Furthermore, the spontaneous formation of LMs (breathers) from thermal fluctuations in lattice systems, when thermalized with the Nosé method [20] has been demonstrated in [21,22]. Here we explain LM formation in a stochastic system involving dissipation in