sine-Gordon模型中旋转对称孤子解的动力学及其在大面积Josephson结方面的应用

DYNAMICS OF ROTATIONALLY SYMMETRIC SINE-GORDON SOL1TONS WITH APPLLCATIONS FOR A LARGE AREA JOSEPHSON JUNCTION

用集体坐标和拉格朗日变分原理为基础的微扰论处理了n+1维旋转对称的sine-Go-rdon孤子在远离原点处受微扰势作用下的行为。强调孤子的粒子性并从正则方法导出其依赖于位置的广义动量和运动方程。这一方法可以处理一类相当广泛的微扰势而无需其具体形式即可定性地讨论孤子的行为。在无耗散条件下,研究了孤子的速度-位置相空间的特性,分析了诸如回波效应、不稳定不动点和逃逸等各种可能的现象。引入耗散后,得到了修正的运动方程。还讨论了上述结果在大面积Josephson结方面的应用,并与数值计算的结果作了比较,两者符合较好。

The dynamics of rotationally symmetric sine Gordon solitons of large radius under poten-tial and dissipative perturbations is considered, with the help of a collective-coordinate desc-ription of the soliton and the Lagrangian variation method. The particle-like character of the soliton is emphasized The equation of motlon and in particular, the general momentum of the soliton are obtained in a canonical manner. It is possible to discuss the dynamics of the soliton even without applying the explicit form of the perturbating potential All dyna-mical regimes in the phase space are explored. Such phenomena as the soliron return effect, soliton escaping and saddle point are addressed In the presence of dissipation, the corrected equation of soliton motion is obtained from the generalized variational equation. Finally, the application of the theoretical treatment is considered for the fluxon dynamics in a circularly symmetric Josephson junction. The analytical results are examined by direct numerical simu-lations, fairly good agreements being achieved. it turns out that the presented ueaMnem provides a reliable description of the dynamics of the sol tons considered.