2005/02/01 by Oliver Muelken, Oliver Mülken, A. Blumen +1
Computer Science · Mathematics · Physics and Astronomy · #Ansatz #Boundary value problem #Computer science #Discrete time and continuous time #Function (biology) #Mathematical physics #Mathematics #Periodic boundary conditions #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum algorithm #Quantum mechanics #Quantum walk #Quantum-Dot Cellular Automata #Spacetime #Statistical physics #Stochastic matrix #Transfer matrix #cond-mat.stat-mech #quant-ph
paper · pdf · doi:10.1103/physreve.71.036128
published as Phys. Rev. E 71, 036128 (2005) · 5 pages, 4 figures; accepted for publication in PRE
arxiv created 2005/02/01 · openalex publication_date 2005/03/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The propagation by continuous-time quantum walks (CTQWs) on one-dimensional lattices shows structures in the transition probabilities between different sites reminiscent of quantum carpets. For a system with periodic boundary conditions, we calculate the transition probabilities for a CTQW by diagonalizing the transfer matrix and by a Bloch function ansatz. Remarkably, the results obtained for the Bloch function ansatz can be related to results from (discrete) generalized coined quantum walks. Furthermore, we show that here the first revival time turns out to be larger than for quantum carpets.