Two-dimensional quantum random walk
| Autor: | Wil Brady, Yuliy Baryshnikov, Andrew Bressler, Robin Pemantle |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2008 |
| Předmět: |
Function field of an algebraic variety
010102 general mathematics Feasible region Mathematical analysis Statistical and Nonlinear Physics Algebraic variety Random walk 05A15 82C10 01 natural sciences 0103 physical sciences FOS: Mathematics Mathematics - Combinatorics Algebraic function Quantum walk Limit (mathematics) Combinatorics (math.CO) 0101 mathematics 010306 general physics Mathematical Physics Mathematics Singular point of an algebraic variety |
| Popis: | 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). |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|