An analytic solution for one-dimensional quantum walks

2007/05/01 by Ian Fuss, Lang White, Fuss, Ian +5 · 1 citation
Physics and Astronomy · #FOS: Physical sciences #Quantum Physics (quant-ph) #quant-ph

paper · pdf · doi:10.48550/arxiv.0705.0077

23 pages

arxiv created 2007/05/01 · arxiv updated 2009/12/01

Abstract

The first general analytic solutions for the one-dimensional walk in position and momentum space are derived. These solutions reveal, among other things, new symmetry features of quantum walk probability densities and further insight into the behaviour of their moments. The analytic expressions for the quantum walk probability distributions provide a means of modelling quantum phenomena that is analogous to that provided by random walks in the classical domain.

Cited by

• Coherent migration of the single excitation injected into finite-length segment of the biomolecular chain

Related

• Momentum Dynamics of One Dimensional Quantum Walks
• Quantum random walks in one dimension
• Intertwining operators between one-dimensional homogeneous quantum walks
• Space-homogeneous quantum walks on Z from the viewpoint of complex analysis
• Categories of quantum walks