Noise Induced Switching Between Oscillation States in a Nonlinear Micromechanical Oscillator

Abstract

The interplay of noise and nonlinearity often leads to novel phenomena in micro- and nano-systems. Such phenomena are of fundamental and practical interest since they have the potential to offer new functionalities and to improve the performance of sensors. For instance, nonlinear systems often develops bistability when the periodic driving is sufficiently strong. In the presence of fluctuations, the nonlinear system can be induced to escape from one metastable dynamical state into the other. Unlike equilibrium systems where the escape rate can be calculated from the height of the free-energy barrier [1], driven systems are, generally, far from thermal equilibrium and cannot be characterized by free energy [2–5]. Consequently, the escape rate in such non-equilibrium systems must be derived from system dynamics [6–9]. Experiments on noise induced switching has been performed in a number of driven nonlinear systems, including parametrically driven electrons in a Penning trap [10], doubly clamped nanomechanical beams [11, 12] and radio frequency driven Josephson junctions [13]. Calculation of the escape rate in such non-equilibrium systems is a non-trivial problem and has attracted much interest [7, 8, 14, 15].