Kink Dynamics in the sine-Gordon Model: Interaction with Inhomogeneities

by Jacek Gatlik

Thursday 21 Dec 2023, 14:00 → 15:00 Europe/Warsaw

4402 (IFJ PAN)

The research focuses on an extensive analysis of the dynamics of kink solutions in a modified sine-Gordon model. They include a comprehensive study of the effects of the breaking of translational invariance by the presence of localized inhomogeneities and the impact of thermal noise. Generalizations to more spatial dimensions were also considered. 
Initially, the sine-Gordon model is modified by a position-dependent dispersive term, relevant for the dynamics of superconducting electrodes in Josephson junctions. This leads to a generalization for junctions of arbitrary curvature. The study critiques traditional collective coordinate descriptions of kink motion, proposing a more accurate approach [1].
Furthermore, the impact of thermal noise on kink propagation, particularly in curved Josephson junctions, is explored. An analytical expression is derived to calculate kink transmission probability over potential barriers, showing high concordance with simulations especially at temperatures above 1K [2].
In a subsequent analysis, the interaction between sine-Gordon kinks and localized inhomogeneities is examined, focusing on the effects of potential energy barriers on kink motion and stability at near-critical velocities. Low-dimensional models are used, demonstrating accuracy in simulating complex physical interactions [3].
Finally, the research investigates the effect of inhomogeneities on kink movement in 2+1 dimensions, developing an equation for kink motion across various scenarios. This provides insights into the spectral features and dynamical interactions of kinks with heterogeneities, with analytical predictions aligning with numerical calculation [4].
The collective findings from these studies not only advance our understanding of kink dynamics in complex media but also pave the way for future research in the domain of non-linear wave motions in dispersive systems. 

[1] J. Gatlik and T. Dobrowolski, Physica D, 428, 133061 (2021).
[2] J. Gatlik and T. Dobrowolski, Physica D, 445, 133649 (2023).
[3] J. Gatlik, T. Dobrowolski, and P. G. Kevrekidis,  Phys. Rev. E, 108, 034203 (2023).
[4] J. Gatlik, T. Dobrowolski, and P. G. Kevrekidis, arXiv:2310.17926 [nlin.PS], (2023).