Dynamics of solitons for nonlinear quantum walks
Dynamics of solitons for nonlinear quantum walks
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DOI：
10.1088/2399-6528/aafe2c
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发表时间：
2018-08
影响因子：
1.2
通讯作者：
Masaya Maeda;Hironobu Sasaki;E. Segawa;A. Suzuki;Kanako Suzuki
中科院分区：
文献类型：
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作者：
Masaya Maeda;Hironobu Sasaki;E. Segawa;A. Suzuki;Kanako Suzuki
我们给出了作者解析研究的非线性量子行走（NLQWs）的一些数值结果（Maeda et al . 2018 Discrete Contin）。Dyn系统38 3687-3703；Maeda et al . 2018 Quantum Inf. Process. 17 215)。结果表明，如果非线性较弱，则NLQWs的长时间行为可以用线性量子行走来近似。在本文中，我们观察到nlqw的线性衰减范围比（Maeda et al . 2018 Discrete Contin）中研究的非线性范围更宽。Dyn. system . 38 3687-3703)。此外，我们还处理了强非线性区域，并证明了解的孤子行为。孤子解有很多种，动力学变得复杂。然而，我们看到有一些特殊的情况，我们可以计算显式形式的解。为了理解非线性动力学，我们系统地研究了孤子解之间的碰撞。我们可以找到模型和非线性微分方程之间的关系。
We present some numerical results for nonlinear quantum walks (NLQWs) studied by the authors analytically (Maeda et al 2018 Discrete Contin. Dyn. Syst. 38 3687–3703; Maeda et al 2018 Quantum Inf. Process. 17 215). It was shown that if the nonlinearity is weak, then the long time behavior of NLQWs are approximated by linear quantum walks. In this paper, we observe the linear decay of NLQWs for range of nonlinearity wider than studied in (Maeda et al 2018 Discrete Contin. Dyn. Syst. 38 3687–3703). In addition, we treat the strong nonlinear regime and show that the solitonic behavior of solutions appears. There are several kinds of soliton solutions and the dynamics becomes complicated. However, we see that there are some special cases so that we can calculate explicit form of solutions. In order to understand the nonlinear dynamics, we systematically study the collision between soliton solutions. We can find a relationship between our model and a nonlinear differential equation.