Spontaneous emission of radiation from a discrete sine-Gordon kink

Mode locking in discrete soliton dynamics under ac forces

“…The first one is the emission of radiation of small-amplitude oscillations ͑linear waves or phonons͒ in the motion of defects. 2,5,6 Recent studies of equations ͑1͒, with constant homogeneous force F, have provided a good quantitative explanation of experimental measurements of the current-voltage characteristics of circular arrays ͑rings͒ of underdamped Josephson junctions biased by constant currents. 7,8 An important outcome from these comparisons between theory and experiments is the essential role played by the discrete character of the model and the finite number of degrees of freedom of the experimental system; in other words, essential aspects of the physical phenomena are lost when a continuum limit of equations ͑1͒ is taken.…”

“…8 The second effect is the pinning of the kink to the underlying discrete lattice. 1,[4][5][6] The kink has to overcome an energy barrier ͓the so-called Peierls-Nabarro ͑PN͒ barrier͔ to start to move; otherwise the soliton stays trapped oscillating with a characteristic frequency, known as the PN frequency. This frequency appears in the gap of the linear waves spectrum and substitutes the zero frequency ͑Goldstone mode͒ associated with the translation invariance of the continuous system.…”

A quantum Peierls-Nabarro barrier

“…One should remember, of course, that in varying h one also varies the shape of the transparent substrate potential V h (which would not otherwise remain transparent). In fact, the limit h → ∞ is always badly singular since the curvature of the substrate at the vacua grows unbounded, by equation (6). …”

“…It can have strong effects on the dynamics of kinks in the system (kink trapping, radiative deceleration, phonon bursts etc. [5,6]). …”

“…Since f (z) has order e −µ|z| exponential decay, V ′′ h (a ± ) is given by equation (6), and the vacuum W -matrix takes the simple form…”