Decay of bound states in a sine-Gordon equation with double well potentials

Ali, Amir; Susanto, Hadi; Wattis, Jonathan A.D.

Abstract

We consider a spatially inhomogeneous sine-Gordon equation with a double-well potential, describing long Josephson junctions with phase-shifts. We discuss the interactions of symmetric and antisymmetric bound states in the system. Using a multiple scale expansion, we show that the modes decay algebraically in time due to the energy transfer from the discrete to the continuous spectrum. In particular, exciting the two modes at the same time yields an increased decay rate. An external time-periodic drive is shown to sustain symmetric state, while it damps the antisymmetric one.

Citation

Ali, A., Susanto, H., & Wattis, J. A. (2015). Decay of bound states in a sine-Gordon equation with double well potentials. Journal of Mathematical Physics, 56, Article 051502. https://doi.org/10.1063/1.4917284

• Journal Article Type: Article
• Publication Date: Jan 1, 2015
• Deposit Date: Nov 12, 2015
• Publicly Available Date: Nov 12, 2015
• Journal: Journal of Mathematical Physics
• Print ISSN: 0022-2488
• Electronic ISSN: 1089-7658
• Publisher: American Institute of Physics
• Peer Reviewed: Peer Reviewed
• Volume: 56
• Article Number: 051502
• DOI: https://doi.org/10.1063/1.4917284
• Public URL: https://nottingham-repository.worktribe.com/output/987607
• Publisher URL: http://scitation.aip.org/content/aip/journal/jmp/56/5/10.1063/1.4917284
• Additional Information: Copyright 2015 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in G. A. Gibson et al., Journal of Mathematical Physics 56, 051502 (2015) http://dx.doi.org/10.1063/1.4917284 and may be found at http://scitation.aip.org/content/aip/journal/jmp/56/5/10.1063/1.4917284.