1992
DOI: 10.1063/1.463812
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A quantum random-walk model for tunneling diffusion in a 1D lattice. A quantum correction to Fick’s law

Abstract: With the help of quantum-scattering-theory methods and the approximation of stationary phase, a one-dimensional coherent random-walk model which describes both tunneling and scattering above the potential diffusion of particles in a periodic one-dimensional lattice is proposed. The walk describes for each lattice cell, the time evolution of modulating amplitudes of two opposite-moving Gaussian wave packets as they are scattered by the potential barriers. Since we have a coherent process, interference contribut… Show more

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Cited by 51 publications
(31 citation statements)
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“…The DL and the ballistic behavior have already been observed experimentally [4,5]. On the other hand the concept of QW introduced in [6,7] is a counterpart of the classical random walk. Its most striking property is its ability to spread over the line linearly in time, this means that the standard deviation grows as σ(t) ∼ t, while in the classical walk it grows as σ(t) ∼ t 1/2 .…”
mentioning
confidence: 88%
“…The DL and the ballistic behavior have already been observed experimentally [4,5]. On the other hand the concept of QW introduced in [6,7] is a counterpart of the classical random walk. Its most striking property is its ability to spread over the line linearly in time, this means that the standard deviation grows as σ(t) ∼ t, while in the classical walk it grows as σ(t) ∼ t 1/2 .…”
mentioning
confidence: 88%
“…We mention, in particular, work of Aharonov et al [24], work of Godoy et al [25,26], and work of Barra and Gaspard [27]. The papers of Godoy and co-authors as well as that of Barra and Gaspard have interesting parallels with ours.…”
Section: Introductionmentioning
confidence: 65%
“…(25). Depending on the sign of cos 2(β + ω) there are two types of solutions: if the frequency of the incident wave falls in one of the quasienergy bands…”
Section: Figmentioning
confidence: 99%
“…This results in the probability distributions of the quantum walker being quite distinct from that of a classical random walker. Ever since their introduction [1][2][3] there has been immense interest in quantum walks [4,5], motivated by the promise of faster execution of a variety of computational tasks [6][7][8][9]. It has now been shown that any quantum circuit can be effectively simulated by continuous [10] or discrete quantum walks [11], making them universal computational primitives.…”
Section: Introductionmentioning
confidence: 99%