Disordered quantum walks in one lattice dimension

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Standard

Disordered quantum walks in one lattice dimension. / Ahlbrecht, Andre; Scholz, Volkher B.; Werner, Albert H.

In: Journal of Mathematical Physics, Vol. 52, No. 10, 102201, 05.10.2011.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Ahlbrecht, A, Scholz, VB & Werner, AH 2011, 'Disordered quantum walks in one lattice dimension', Journal of Mathematical Physics, vol. 52, no. 10, 102201. https://doi.org/10.1063/1.3643768

APA

Ahlbrecht, A., Scholz, V. B., & Werner, A. H. (2011). Disordered quantum walks in one lattice dimension. Journal of Mathematical Physics, 52(10), [102201]. https://doi.org/10.1063/1.3643768

Vancouver

Ahlbrecht A, Scholz VB, Werner AH. Disordered quantum walks in one lattice dimension. Journal of Mathematical Physics. 2011 Oct 5;52(10). 102201. https://doi.org/10.1063/1.3643768

Author

Ahlbrecht, Andre ; Scholz, Volkher B. ; Werner, Albert H. / Disordered quantum walks in one lattice dimension. In: Journal of Mathematical Physics. 2011 ; Vol. 52, No. 10.

Bibtex

@article{a51af03b9010451ba20a76674f50e642,
title = "Disordered quantum walks in one lattice dimension",
abstract = "We study a spin-1/2-particle moving on a one-dimensional lattice subject to disorder induced by a random, space-dependent quantum coin. The discrete time evolution is given by a family of random unitary quantum walk operators, where the shift operation is assumed to be deterministic. Each coin is an independent identically distributed random variable with values in the group of two-dimensional unitary matrices. We derive sufficient conditions on the probability distribution of the coins such that the system exhibits dynamical localization. Put differently, the tunneling probability between two lattice sites decays rapidly for almost all choices of random coins and after arbitrary many time steps with increasing distance. Our findings imply that this effect takes place if the coin is chosen at random from the Haar measure, or some measure continuous with respect to it, but also for a class of discrete probability measures which support consists of two coins, one of them being the Hadamard coin.",
author = "Andre Ahlbrecht and Scholz, {Volkher B.} and Werner, {Albert H.}",
year = "2011",
month = oct,
day = "5",
doi = "10.1063/1.3643768",
language = "English",
volume = "52",
journal = "Journal of Mathematical Physics",
issn = "0022-2488",
publisher = "A I P Publishing LLC",
number = "10",

}

RIS

TY - JOUR

T1 - Disordered quantum walks in one lattice dimension

AU - Ahlbrecht, Andre

AU - Scholz, Volkher B.

AU - Werner, Albert H.

PY - 2011/10/5

Y1 - 2011/10/5

N2 - We study a spin-1/2-particle moving on a one-dimensional lattice subject to disorder induced by a random, space-dependent quantum coin. The discrete time evolution is given by a family of random unitary quantum walk operators, where the shift operation is assumed to be deterministic. Each coin is an independent identically distributed random variable with values in the group of two-dimensional unitary matrices. We derive sufficient conditions on the probability distribution of the coins such that the system exhibits dynamical localization. Put differently, the tunneling probability between two lattice sites decays rapidly for almost all choices of random coins and after arbitrary many time steps with increasing distance. Our findings imply that this effect takes place if the coin is chosen at random from the Haar measure, or some measure continuous with respect to it, but also for a class of discrete probability measures which support consists of two coins, one of them being the Hadamard coin.

AB - We study a spin-1/2-particle moving on a one-dimensional lattice subject to disorder induced by a random, space-dependent quantum coin. The discrete time evolution is given by a family of random unitary quantum walk operators, where the shift operation is assumed to be deterministic. Each coin is an independent identically distributed random variable with values in the group of two-dimensional unitary matrices. We derive sufficient conditions on the probability distribution of the coins such that the system exhibits dynamical localization. Put differently, the tunneling probability between two lattice sites decays rapidly for almost all choices of random coins and after arbitrary many time steps with increasing distance. Our findings imply that this effect takes place if the coin is chosen at random from the Haar measure, or some measure continuous with respect to it, but also for a class of discrete probability measures which support consists of two coins, one of them being the Hadamard coin.

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U2 - 10.1063/1.3643768

DO - 10.1063/1.3643768

M3 - Journal article

AN - SCOPUS:80055114083

VL - 52

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 10

M1 - 102201

ER -

ID: 256316737