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APS » Journals » Phys. Rev. D » Volume 71 » Issue 2
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Phys. Rev. D 71, 024029 (2005) [15 pages]

Random walk in generalized quantum theory

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Xavier Martin1, Denjoe O’Connor1,2, and Rafael D. Sorkin3,4
1School of Theoretical Physics, DIAS, 10 Burlington Road, Dublin 4, Ireland
2Depto de Física, Cinvestav, Apartado Postal 70-543, México D.F. 0730.
3Perimeter Institute, Waterloo, Ontario, Canada N2J 2W9
4Dept. of Physics, Syracuse University, Syracuse, New York, 13244-1130, USA

Received 17 June 2004; published 25 January 2005

One can view quantum mechanics as a generalization of classical probability theory that provides for pairwise interference among alternatives. Adopting this perspective, we “quantize” the classical random walk by finding, subject to a certain condition of “strong positivity”, the most general Markovian, translationally invariant “decoherence functional” with nearest neighbor transitions.

© 2005 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevD.71.024029
DOI:
10.1103/PhysRevD.71.024029
PACS:
04.60.Nc, 03.65.Ta, 05.40-a, 05.40.Fb
 
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