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Synchronization of a Josephson junction array in terms of global variables
Vladimir Vlasov1, Arkady Pikovsky
1Department of Physics and Astronomy, Potsdam University, 14476 Potsdam, Germany.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 17, 2013
Summary
This study analyzes Josephson junction arrays using the Watanabe-Strogatz approach. It reveals bistability in synchronous and asynchronous states for identical junctions and explores transitions in disordered arrays.
Area of Science:
- Condensed Matter Physics
- Nonlinear Dynamics
- Superconductivity
Background:
- Josephson junction arrays are crucial in superconducting electronics.
- Understanding their collective dynamics, including synchronous and asynchronous states, is essential.
- The Watanabe-Strogatz approach offers a method to simplify complex many-body dynamics.
Purpose of the Study:
- To apply the Watanabe-Strogatz approach to Josephson junction arrays with a common LCR load.
- To analyze the dynamics and stability of synchronous and asynchronous states.
- To investigate the transition between synchrony and asynchrony in both identical and disordered arrays.
Main Methods:
- Utilized the Watanabe-Strogatz approach to reduce array dynamics to global variables.
- Formulated a finite set of equations for identical Josephson junctions.
- Developed an integro-differential equation for disordered arrays and employed numerical methods for stability analysis.
Main Results:
- Identified regions of bistability between synchronous and asynchronous states for identical junctions.
- Established the stability of asynchronous states in disordered arrays.
- Numerically characterized the transition properties between synchrony and asynchrony in disordered systems.
Conclusions:
- The Watanabe-Strogatz approach effectively simplifies the analysis of Josephson junction array dynamics.
- Bistability and stability phenomena are key characteristics of these arrays.
- Numerical analysis is vital for understanding complex transitions in disordered superconducting systems.
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