# Resonant-tunneling in discrete-time quantum walk

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## Abstract

We show that discrete-time quantum walks on the line, \(\mathbb {Z}\), behave as “the quantum tunneling”. In particular, quantum walkers can tunnel through a double-well with the transmission probability 1 under a mild condition. This is a property of quantum walks which cannot be seen on classical random walks, and is different from both linear spreadings and localizations.

## Keywords

Quantum walk Quantum mechanics Resonant-tunneling Stationary measures## Notes

### Acknowledgements

The authors would like to thank N. Konno for his kind discussion. This work was supported by JSPS KAKENHI Grant numbers JP17K14235, JP17H04978, JP24540208, JP16K05227, JP16K17637, and JP16K03939. KM was partially supported by Program for Promoting the reform of national universities (Kyushu University), Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan, World Premier International Research Center Initiative (WPI), MEXT, Japan.

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