Three routes to the exact asymptotics for the one-dimensional quantum walk

Journal of Physics A: Mathematical and General

Volumn 36, Issue 33, 2003, Pages 8775-8795

  Carteret, Hilary A ^a   Ismail, Mourad E H ^b   Richmond, Bruce ^a  

^a UNIVERSITY OF WATERLOO   (Canada)

^b UNIVERSITY OF CENTRAL FLORIDA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0242298101     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/36/33/305     Document Type: Article

References (16)

1. Abramowitz Milton and Stegun Irene A (ed) 1974 Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables (New York: Dover)
2. Aharonov Y, Davidovich L and Zagury N 1993 Quantum random walks Phys. Rev. A 48 1687
3. Ambainis A, Bach E, Nayak A, Vishwanath A and Watrous J One-dimensional quantum walks Proc. ACM Symp. on Theory of Computation (STOC'01) (July 2001) (New York: Association for Computing Machinery) pp 37-49
4. Andrews G E, Askey R A and Roy R 1999 Special Functions (Cambridge: Cambridge University Press)
5. Arfken George B and Weber Hans-Jurgen 2000 Mathematical Methods for Physicists 5th edn (New York: Academic)
6. Brun T A, Carteret H A and Ambainis A 2002 Quantum walks driven by many coins Preprint quant-ph/0210161 (Phys. Rev. A at press)
7. Chen L-D and Ismail M E H 1991 On asymptotics of Jacobi polynomials SIAM J. Math. Anal. 22 1442-9
8. Feynman R P and Hibbs A R 1965 Quantum Mechanics and Path Integrals (New York: McGraw-Hill)
9. an+α,bn+β (New York: Academic) pp 379-404
10. McClure J P and Wong R 1997 Justification of the stationary phase approximation in time-domain asymptotics Proc. R. Soc. A. 453 1019-31
11. Meyer David A 1996 From quantum cellular automata to quantum lattice gases J. Stat. Phys. 85 551-74 (Preprint quant-ph/9604003)
12. Nayak Ashwin and Vishwanath Ashvin 2000 Quantum walk on the line Preprint quant-ph/0010117
13. Olver Frank W J 1997 Asymptotics and Special Functions (AKP Classics)
14. Saff E B and Varga R S The sharpness of Lorentz's theorem on incomplete polynomials Trans. Am. Math. Soc. 249 163-86
15. Szegö G 1975 Orthogonal Polynomials 4th edn (Providence, RI: American Mathematical Society)
16. Wong Roderick 2001 Asymptotic Approximations of Integrals 2nd edn SIAM Classics in Applied Mathematics vol 34 (Society for Industrial and Applied Mathematics)