Abstract
We investigate noise-induced transitions in a current-biased and weakly damped Josephson junction in the presence of multiplicative noise. By using the stochastic averaging procedure, the averaged amplitude equation describing dynamic evolution near a constant phase difference is derived. Numerical results show that a stochastic Hopf bifurcation between an absorbing and an oscillatory state occurs. This means the external controllable noise triggers a transition into the non-zero junction voltage state. With the increase of noise intensity, the stationary probability distribution peak shifts and is characterised by increased width and reduced height. And the different transition rates are shown for large and small bias currents.
Highlights
Nonlinear dynamics in Josephson junctions (JJs) are interesting to investigate both from experimental and theoretical points of view
The escape rates describing the relationship between the transition of distribution peak and the change of noise strength are obtained for different bias currents
Noise induced quantum phase diffusions were experimentally observed in the underdamped JJ,[1] and the escape rates in zero and finite magnetic fields were investigated in thermal regime.[2]
Summary
Nonlinear dynamics in Josephson junctions (JJs) are interesting to investigate both from experimental and theoretical points of view. Noise induced quantum phase diffusions were experimentally observed in the underdamped JJ,[1] and the escape rates in zero and finite magnetic fields were investigated in thermal regime.[2] When temperatures close to the transition thresholds, the escape rate was determined from the distribution of the critical currents. This paper focuses on a theoretical and numerical investigation of stochastic bifurcations triggered by external noise near zero voltage state. Since the amplitude is a slowly varying process, the averaged equation is obtained by the stochastic averaging method for the weakly perturbed system and the probability distribution of amplitude is simulated numerically after long time evolution.
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