Two-dimensional Quantum Random Walk
Identifieur interne : 003003 ( Main/Exploration ); précédent : 003002; suivant : 003004Two-dimensional Quantum Random Walk
Auteurs : Yuliy Baryshnikov [États-Unis] ; Wil Brady [États-Unis] ; Andrew Bressler [États-Unis] ; Robin Pemantle [États-Unis]Source :
- Journal of Statistical Physics [ 0022-4715 ] ; 2011-01-01.
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Abstract
Abstract: We analyze several families of two-dimensional quantum random walks. The feasible region (the region where probabilities do not decay exponentially with time) grows linearly with time, as is the case with one-dimensional QRW. The limiting shape of the feasible region is, however, quite different. The limit region turns out to be an algebraic set, which we characterize as the rational image of a compact algebraic variety. We also compute the probability profile within the limit region, which is essentially a negative power of the Gaussian curvature of the same algebraic variety. Our methods are based on analysis of the space-time generating function, following the methods of Pemantle and Wilson (J. Comb. Theory, Ser. A 97(1):129–161, 2002).
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DOI: 10.1007/s10955-010-0098-2
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The feasible region (the region where probabilities do not decay exponentially with time) grows linearly with time, as is the case with one-dimensional QRW. The limiting shape of the feasible region is, however, quite different. The limit region turns out to be an algebraic set, which we characterize as the rational image of a compact algebraic variety. We also compute the probability profile within the limit region, which is essentially a negative power of the Gaussian curvature of the same algebraic variety. Our methods are based on analysis of the space-time generating function, following the methods of Pemantle and Wilson (J. Comb. Theory, Ser. A 97(1):129–161, 2002).</div></front></TEI><affiliations><list><country><li>États-Unis</li></country><region><li>New Jersey</li><li>Pennsylvanie</li><li>Washington (État)</li></region></list><tree><country name="États-Unis"><region name="New Jersey"><name sortKey="Baryshnikov, Yuliy" sort="Baryshnikov, Yuliy" uniqKey="Baryshnikov Y" first="Yuliy" last="Baryshnikov">Yuliy Baryshnikov</name></region><name sortKey="Brady, Wil" sort="Brady, Wil" uniqKey="Brady W" first="Wil" last="Brady">Wil Brady</name><name sortKey="Bressler, Andrew" sort="Bressler, Andrew" uniqKey="Bressler A" first="Andrew" last="Bressler">Andrew Bressler</name><name sortKey="Bressler, Andrew" sort="Bressler, Andrew" uniqKey="Bressler A" first="Andrew" last="Bressler">Andrew Bressler</name><name sortKey="Pemantle, Robin" sort="Pemantle, Robin" uniqKey="Pemantle R" first="Robin" last="Pemantle">Robin Pemantle</name><name sortKey="Pemantle, Robin" sort="Pemantle, Robin" uniqKey="Pemantle R" first="Robin" last="Pemantle">Robin Pemantle</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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