Resonance Effects on the Lifetime of Nonequilibrium Steady States in a Forced Pendulum Driven by a Quasi-Monochromatic Noise
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概要
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A damped pendulum has two classes of steady states under the action of a constant external torque and friction torque proportional to its angular velocity. That is, nonequilibrium steady states (NSSs) and metastable equilibrium states (MESs). In a NSS the pendulum rotates steadily in the direction of the constant external torque which is balanced with the friction one, and the time average of the angular velocity of the pendulum is neither steadily accelerated nor decelerated, but remains constant. On the other hand, in a MSS the pendulum is at rest at a metastable equilibrium position. If the pendulum is also driven by thermal noise, however, transitions between the two classes of steady states occur. Resistively shunted Josephson junctions are modeled by the equation of motion for the pendulum. In this paper, the lifetime of a NSS, namely, the time to elapse in the NSS before a transition to a MES, is investigated with special attention to resonance phenomena under the influence of a quasi-monochromatic random torque (noise), which has a characteristic frequency. With computer simulation, we find the resonance phenomena that the mean lifetime as a function of the characteristic noise frequency has a minimum for a frequency close to the characteristic frequency of the motion in the NSS. We theoretically derive the mean lifetime and the activation energy for escape from the NSS with the probability distribution function of an action variable calculated with Carmeli and Nitzan's reduction procedure in a low friction and small external torque limit. Making a comparison between theoretical and simulation results, we have good agreement between them.
- 2011-04-15
著者
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Igarashi Akito
Department Of Applied Mathematics And Physics Faculty Of Engineering Kyoto University
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Igarashi Akito
Department of Applied Mathematics and Physics, Kyoto University, Kyoto 606-8501, Japan
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Asai Yousuke
Department of Applied Mathematics and Physics, Kyoto University, Kyoto 606-8501, Japan
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