2008/07/13 by Mark S. Rudner, M. S. Rudner, Leonid Levitov +1 · 2 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum and electron transport phenomena #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevlett.102.065703
4 pages, 3 figures
arxiv created 2008/07/13 · openalex publication_date 2009/02/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We analyze a quantum walk on a bipartite one-dimensional lattice, in which the particle can decay whenever it visits one of the two sublattices. The corresponding non-Hermitian tight-binding problem with a complex potential for the decaying sites exhibits two different phases, distinguished by a winding number defined in terms of the Bloch eigenstates in the Brillouin zone. We find that the mean displacement of a particle initially localized on one of the nondecaying sites can be expressed in terms of the winding number, and is therefore quantized as an integer, changing from zero to one at the critical point. We show that the topological transition is relevant for a variety of experimental settings. The quantized behavior can be used to distinguish coherent from incoherent dynamics.