13,728 research outputs found
NORMAL-MODES IN A SOLITARY WAVE SOLUTION TO A DOUBLE SINE-GORDON EQUATION
No full textIn a double sine-Gordon system the internal oscillations of a solitary wave solution can be viewed as normal modes in a number of sine-Gordon 2π-kinks and the ratio between the frequencies can be predicted. For three 2π-kinks this ration is √3
LONG JOSEPHSON-JUNCTIONS PHASE LOCKED TO MICROWAVES BY VARIOUS COUPLINGS
No full textWe have investigated theoretically the heights of the phase locked steps for long Josephson junctions biased on a zero field step for different microwave couplings. We find excellent agreement between the theory and numerical experiments
STABILIZATION OF CHAOTIC PHASE-LOCKED DYNAMICS IN LONG JOSEPHSON-JUNCTIONS
No full textWe study the stabilization phenomenon of chaotic phase locked dynamics in long Josephson junctions by means of biharmonic drivers. In particular the dependence of the stability range of the equal time of flight solution on the relative phase of the external drivers is derived. The analysis is based on a previously derived phase-locked map and is compared with direct numerical experiments. An experiment to detect the chaos suppression phenomenon in long Josephson junctions is also suggested
Internal oscillation frequencies and anharmonic effects for the double sine-Gordon kink
No full textA simple derivation of the small oscillation frequency around 4π-kink solutions of the double sine-Gordon equation is presented. Small corrections to these frequencies due to anharmonic effects are also numerically and analytically investigated. The analysis is based on energetic considerations and on the mechanical interpretation of a 4π kink as two point particles connected by a spring
PARAMETRIC ADIABATIC PERTURBATIONS ON THE SINE-GORDON BREATHER SOLUTION
No full textBreather dynamics in the sine-Gordon system with changing sine term coefficient is investigated. It is shown that for adiabatic changes the frequency of the breather in rescaled time is constant while the velocity changes just as the velocity of a kink
FLUXON REFLECTION AT LOADED TERMINATIONS OF LONG JOSEPHSON-JUNCTIONS
No full textThe reflection process of fluxons at loaded terminations of long lossless Josephson junctions is examined numerically. The energy absorbed by the load, modelling an external circuit, is calculated and compared to an approximate analytical expression. Further an estimate of the energy of the radiation into the junction resulting from the reflection is calculated. The absorbed energy and the energy of the radiation increase linearly and quadratically with the reciprocal load, respectively
THERMAL SINE-GORDON SYSTEM IN THE PRESENCE OF DIFFERENT TYPES OF DISSIPATION
No full textThe effects of thermal fluctuations on solitons and phonons of the sine-Gordon system are investigated in the presence of a αφt-βφxxt dissipation. The analysis requires the assumption of a more general autocorrelation function for the noise than the one used in previous works. We verify that this leads to the correct results for the average kinetic energies of solitons and phonons in the system. We also evaluate the linewidth for a Josephson oscillator in the presence of both α and β dissipation, and lastly we briefly discuss the extension of the theory to more general dissipative terms
Phonons and solitons in the "thermal" sine-Gordon system
No full textStandard methods of stochastic processes are used to study the coupling of the sine-Gordon system with a heat reservoir. As a result we find thermal phonons with an average energy of kB T per mode. The translational mode (zero mode) is found to carry an average energy of 1 / 2kBT. This last value is just the energy in the Brownian motion of a thermal soliton. These results are in agreement with those obtained by the use of a statistical-mechanical description of a dilute soliton gas. Connection of the above results with Josephson junctions and the extension of the analysis to more general equations is also discussed
Relaxation towards phase-locked dynamics in long Josephson junctions
No full textWe study the relaxation phenomenon towards phase-locked dynamics in long Josephson junctions. In particular the dependence of the relaxation frequency for the equal time of flight solution on the junction parameters is derived. The analysis is based on a phase-locked map and is compared with direct numerical experiments performed both on the map and on the perturbed sine-Gordon equation. As an interesting result we find that very close to a bifurcation the relaxation frequency is exactly equal to the half of the step frequency, i.e., the frequency characterizing the period-one solution
Effect of thermal noise on the phase locking of a Josephson fluxon oscillator
No full textThe influence of thermal noise on fluxon motion in a long Josephson junction is investigated when the motion is phase locked to an external microwave signal. It is demonstrated that the thermal noise can be treated theoretically within the context of a two-dimensional map that models the dynamics of a single fluxon
- …
