Scattering Expansion for Localization in One Dimension: from Disordered Wires to Quantum Walks
arXiv:2211.13368 · doi:10.1103/PhysRevB.109.064201
Abstract
We present a perturbative approach to disordered systems in one spatial dimension that accesses the full range of phase disorder and clarifies the connection between localization and phase information. We consider a long chain of identically disordered scatterers and expand in the reflection strength of any individual scatterer. We apply this expansion to several examples, including the Anderson model, a general class of periodic-on-average-random potentials, and a two-component discrete-time quantum walk, showing analytically in the latter case that the localization length can depend non-monotonically on the strength of phase disorder (whereas expanding in weak disorder yields monotonic decrease). More generally, we obtain to all orders in the expansion a particular non-separable form for the joint probability distribution of the transmission coefficient logarithm and reflection phase. Furthermore, we show that for weak local reflection strength, a version of the scaling theory of localization holds: the joint distribution is determined by just three parameters.
arXiv comment25+19 pages, 9 figures, longer version of arXiv:2210.07999; minor corrections, published version
References in corpus (40)
- Quantum random walks - an introductory overview
- Universal computation by quantum walk
- Quantum walks: a comprehensive review
- Realization of quantum walks with negligible decoherence in waveguide lattices
- Universal quantum computation using the discrete time quantum walk
- Anderson localization of entangled photons in an integrated quantum walk
- Decoherence and disorder in quantum walks: From ballistic spread to localization
- Anomalous Localization in Low-Dimensional Systems with Correlated Disorder
- Quantum walk on the line as an interference phenomenon
- Implementation of quantum search algorithm using classical Fourier optics
- Quantum search without entanglement
- Single parameter scaling in one-dimensional localization revisited
- Quantum Walks on a Random Environment
- Optimizing the discrete time quantum walk using a SU(2) coin
- Localization and its consequences for quantum walk algorithms and quantum communication
- Topological phases and delocalization of quantum walks in random environments
- Statistics of Lyapunov exponent in 1-D random periodic-on-average systems
- Delocalization in random polymer models
- Disordered Quantum Walks in one lattice dimension
- Measuring Topological Invariants in Disordered Discrete Time Quantum Walks
- Band-center anomaly of the conductance distribution in one-dimensional Anderson localization
- Single parameter scaling in 1-D Anderson localization. Exact analytical solution
- Scattering theory of topological phases in discrete-time quantum walks
- Anderson localization in generalized discrete time quantum walks
- Quantum computation with classical light: implementation of the Deutsch-Jozsa Algorithm
- One-Dimensional Kronig-Penney Model with Positional Disorder: Theory versus Experiment
- Anderson localization in metamaterials and other complex media
- Universal quantum computing using single-particle discrete-time quantum walk
- Localized quantum walks as secured quantum memory
- Periodically, Quasi-periodically, and Randomly Driven Conformal Field Theories (II): Furstenberg's Theorem and Exceptions to Heating Phases
- Localization and diffusion in Ising-type quantum networks
- Anderson localization of one-dimensional hybrid particles
- Perturbative test of single parameter scaling for 1D random media
- Relation between Anderson- and Invariant Imbedding Models for Transport in Finite Chains and Study of Phase- and Delay Time Distributions for Strong Disorder
- Transparent mirror effect in twist-angle-disordered bilayer graphene
- Anderson localization in a partially random Bragg grating and a conserved area theorem
- Enhanced quantum tunnelling induced by disorder
- Disorder engineering: From structural coloration to acoustic filters
- Coherent resistance of a disordered 1D wire: Expressions for all moments and evidence for non-Gaussian distribution
- Scattering Expansion for Localization in One Dimension