An analytical study of quantum walk through glued-tree graphs. (12th August 2015)

• Record Type: Journal Article
• Authors: Li, Zhi-Jian; Wang, J B
• Is Part Of: Journal of physics. Volume 48:Number 35(2015)
• Publication Date: 2015-08-12
• Subjects: quantum walk -- resonance tunnelling -- bound eigenstate; 03.67.Lx -- 05.40.Fb -- 05.45.Mt; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8113/48/35/355301
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: In this paper, we analytically investigated the transmission properties of continuous time quantum walks through two types of glued-tree graphs. By mapping the glued-tree graphs onto a non-uniform lattice line, we obtained their bound eigen-energies, which provided a clear and quantitative understanding of the associated resonant transmission behaviours. We also observed interesting zero-mode resonant transmissions, which correspond to zero-energy bound states, for both types of glued-tree graphs with classical Markov transition matrix parameters. By changing the system parameters at the glued nodes, we are able to control the position of the resonant tunnelling peaks.