Continuous time quantum walks in phase space

Abstract

We formulate continuous time quantum walks (CTQW) in a discrete quantum mechanical phase space. We define and calculate the Wigner function (WF) and its marginal distributions for CTQWs on circles of arbitrary length $N$. The WF of the CTQW shows characteristic features in phase space. Revivals of the probability distributions found for continuous and for discrete quantum carpets do manifest themselves as characteristic patterns in phase space.

slightly revised version to be published in PRA, 6 pages, 6 color figures (high quality postscript figures are available upon request)

References in corpus (8)

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• Wigner function for a particle in an infinite lattice
• Continuous-Time Quantum Walks and Trapping
• Investigation of continuous-time quantum walk on root lattice $A_n$ and honeycomb lattice
• Non-equilibrium transition from dissipative quantum walk to classical random walk
• Directed excitation transfer in vibrating chains by external fields
• The effect of large-decoherence on mixing-time in Continuous-time quantum walks on long-range interacting cycles
• Phase space patterns of quantum transport on ordered and disordered networks
• Local subgraph structure can cause localization in continuous-time quantum walk
• Distributions of continuous-time quantum walks