2018
DOI: 10.1007/s40509-017-0151-9
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Resonant-tunneling in discrete-time quantum walk

Abstract: We show that discrete-time quantum walks on the line, 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.

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Cited by 14 publications
(16 citation statements)
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“…Then the unitarity of S 2 (ξ) implies that the perfect transmitting happens iff 1 + ∆e −2iξ = 0. This condition agrees with the result on [13].…”
Section: Then the Eignequation (Esupporting
confidence: 92%
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“…Then the unitarity of S 2 (ξ) implies that the perfect transmitting happens iff 1 + ∆e −2iξ = 0. This condition agrees with the result on [13].…”
Section: Then the Eignequation (Esupporting
confidence: 92%
“…The Fourier transform of Σ gives an explicit formula of the S-matrix determined by the matrix C x . Moreover, our arguments are deeply related with the resonant-tunneling of QWs (see [13]). Precisely, a generalized eigenfunction of U will be constructed in ℓ ∞ (Z; C 2 ) (see [6]), and the S-matrix Σ(θ) appears in this eigenfunction.…”
Section: Introductionmentioning
confidence: 82%
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“…In this paper, we tend to extend the model from that in [19]: (1) we generalize the connected finite graph, the internal graph; (2) we increase the number of tails, that is, the number of directions for observing the behaviour of scattering on the internal; (3) we observe the distribution of penetration into the internal, that is, a kind of conditional probability on the internal. In the next section, using a simple example, the internal graph is a 3-cycle with two tails, we demonstrate and illustrate what we intend.…”
Section: Introductionmentioning
confidence: 99%
“…Roughly speaking, the generalized eigenfunction is not in H but in ℓ ∞ (Z; C 2 ). This is a generalization of tunneling solutions of DTQWs given in [24]. The S-matrix will be represented by the distorted Fourier transformation and the generalized eigenfunction.…”
Section: 2mentioning
confidence: 99%