期刊
JOURNAL OF PHYSICS COMMUNICATIONS
卷 3, 期 7, 页码 -出版社
IOP PUBLISHING LTD
DOI: 10.1088/2399-6528/aafe2c
关键词
quantum walks; nonlinear dynamics; solitons
资金
- JSPS KAKENHI [JP26800054, JP18K03327, JP15K17568, JP17H02851, JP17H02853, JP17K05311]
- Japan Society for the Promotion of Science [16K17637, 16K03939]
- JSPS [26400156, 18K03354]
- Grants-in-Aid for Scientific Research [18K03354, 26400156] Funding Source: KAKEN
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.
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