An Analytical study of quantum walk through glued-tree graphs

Zhi Jian Li, J. B. Wang

Research output: Contribution to journalArticle

8 Citations (Scopus)

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.

Original languageEnglish
Article number355301
Pages (from-to)1-15
Number of pages15
JournalJournal of Physics A: Mathematical and Theoretical
Volume48
Issue number35
DOIs
Publication statusPublished - 12 Aug 2015
Externally publishedYes

Keywords

  • bound eigenstate
  • quantum walk
  • resonance tunnelling

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