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Article

# A Discontinuity of the Energy of Quantum Walk in Impurities

1
Department of Mathematical Sciences, Ritsumeikan University/Noji-Higashi, Kusatsu 525-8577, Japan
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Math. Research Institute Calc for Industry/Minami, Hiroshima 732-0816, Japan
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Department of Applied Mathematics, Yokohama National University/Hodogaya, Yokohama 240-8501, Japan
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Graduate School of Science and Engineering, Ehime University/Bunkyo-cho 3, Matsuyama, Ehime 790-8577, Japan
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Graduate School of Environment Information Sciences, Yokohama National University/Hodogaya, Yokohama 240-8501, Japan
*
Author to whom correspondence should be addressed.
Academic Editor: Motoichi Ohtsu
Symmetry 2021, 13(7), 1134; https://doi.org/10.3390/sym13071134
Received: 29 May 2021 / Revised: 17 June 2021 / Accepted: 21 June 2021 / Published: 24 June 2021
(This article belongs to the Special Issue Quantum Fields and Off-Shell Sciences)
We consider the discrete-time quantum walk whose local dynamics is denoted by a common unitary matrix C at the perturbed region $\left\{0,1,\cdots ,M-1\right\}$ and free at the other positions. We obtain the stationary state with a bounded initial state. The initial state is set so that the perturbed region receives the inflow ${\omega }^{n}$ at time n$\left(|\omega |=1\right)$. From this expression, we compute the scattering on the surface of $-1$ and M and also compute the quantity how quantum walker accumulates in the perturbed region; namely, the energy of the quantum walk, in the long time limit. The frequency of the initial state of the influence to the energy is symmetric on the unit circle in the complex plain. We find a discontinuity of the energy with respect to the frequency of the inflow. View Full-Text
Keywords:
MDPI and ACS Style

Higuchi, K.; Komatsu, T.; Konno, N.; Morioka, H.; Segawa, E. A Discontinuity of the Energy of Quantum Walk in Impurities. Symmetry 2021, 13, 1134. https://doi.org/10.3390/sym13071134

AMA Style

Higuchi K, Komatsu T, Konno N, Morioka H, Segawa E. A Discontinuity of the Energy of Quantum Walk in Impurities. Symmetry. 2021; 13(7):1134. https://doi.org/10.3390/sym13071134

Chicago/Turabian Style

Higuchi, Kenta, Takashi Komatsu, Norio Konno, Hisashi Morioka, and Etsuo Segawa. 2021. "A Discontinuity of the Energy of Quantum Walk in Impurities" Symmetry 13, no. 7: 1134. https://doi.org/10.3390/sym13071134

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