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arXiv 0807.3181cond-mat.supr-concond-mat.mes-hall
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动态Cooper配对理论中的正常孤子和反常孤子

Normal and anomalous solitons in the theory of dynamical Cooper pairing

Emil A. Yuzbashyan

摘要:

我们得到的多孤子解的时间相关的Bogoliubov-德Gennes方程,或等价地,Gorkov方程描述的动力学的费米子凝聚体中的耗散制度。有两种类型的孤子-正常和反常。在大的时间,正常的多孤子渐近BCS哈密顿量的不稳定的定态与零序参量(正常状态),而反常的倾向于特征在于一个非零的反常平均的本征态。在某些情况下,多孤子解分裂成单孤子的和。在定态附近的线性分析中,孤子对应于不稳定模。一般来说,它们是这些模式的非线性扩展,因此具有$k$不稳定模式的定态产生$k$ -孤子解。我们将多孤子的参数与渐近定态的参数联系起来,从而确定了激发孤子所需的条件。我们进一步指出,在许多物理情况下的动力学是多孤子。

英文摘要:

We obtain multi-soliton solutions of the time-dependent Bogoliubov-de Gennes equations or, equivalently, Gorkov equations that describe the dynamics of a fermionic condensate in the dissipationless regime. There are two kinds of solitons - normal and anomalous. At large times, normal multi-solitons asymptote to unstable stationary states of the BCS Hamiltonian with zero order parameter (normal states), while the anomalous ones tend to eigenstates characterized by a nonzero anomalous average. Under certain circumstances, multi-soliton solutions break up into sums of single solitons. In the linear analysis near the stationary states, solitons correspond to unstable modes. Generally, they are nonlinear extensions of these modes, so that a stationary state with $k$ unstable modes gives rise to a $k$-soliton solution. We relate parameters of the multi-solitons to those of the asymptotic stationary state, which determines the conditions necessary for exciting solitons. We further argue that the dynamics in many physical situations is multi-soliton.

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