无反射势垒散射暗孤子的量子反射和位置相关色散
Quantum reflection of dark solitons scattered by reflectionless potential barrier and position-dependent dispersion
摘要：
本文从理论上和数值上研究了暗孤子通过无反射势垒和存在位置相关色散时的量子反射。我们证实，量子反射发生在这两种情况下，完全反射和完全传输之间的急剧转变，在一个临界的初始孤子速度。根据孤子参数和势参数，对临界速度进行了数值和解析计算。临界转速的解析表达式推导出使用精确的捕获模式，一个时间无关的，和一个时间相关的变分计算。然后，它表明，共振散射发生在临界速度，入射孤子的能量是共振的捕获模式。只要避免周期性的多孤子喷射制度的临界速度的分析和数值之间的合理协议。
英文摘要：
We investigate theoretically and numerically quantum reflection of dark solitons propagating through an external reflectionless potential barrier or in the presence of a position-dependent dispersion. We confirm that quantum reflection occurs in both cases with sharp transition between complete reflection and complete transmission at a critical initial soliton speed. The critical speed is calculated numerically and analytically in terms of the soliton and potential parameters. Analytical expressions for the critical speed were derived using the exact trapped mode, a time-independent, and a time-dependent variational calculations. It is then shown that resonant scattering occurs at the critical speed, where the energy of the incoming soliton is resonant with that of a trapped mode. Reasonable agreement between analytical and numerical values for the critical speed is obtained as long as a periodic multi-soliton ejection regime is avoided.
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