Quantum walks with an anisotropic coin II: scattering theory
arXiv:1801.02779 · doi:10.1007/s11005-018-1100-1
Abstract
We perform the scattering analysis of the evolution operator of quantum walks with an anisotropic coin, and we prove a weak limit theorem for their asymptotic velocity. The quantum walks that we consider include one-defect models, two-phase quantum walks, and topological phase quantum walks as special cases. Our analysis is based on an abstract framework for the scattering theory of unitary operators in a two-Hilbert spaces setting, which is of independent interest.
23 pages
References in corpus (3)
Cited by in corpus (21)
- Quantum walks with an anisotropic coin I: spectral theory
- Localization for a one-dimensional split-step quantum walk with bound states robust against perturbations
- Generalized eigenfunctions and scattering matrices for position-dependent quantum walks
- Continuous limits of linear and nonlinear quantum walks
- Weak limit theorem for a one-dimensional split-step quantum walk
- The Witten Index for 1D Supersymmetric Quantum Walks with Anisotropic Coins
- A Constructive Approach to Topological Invariants for One-dimensional Strictly Local Operators
- Eigenvalues of two-phase quantum walks with one defect in one dimension
- Absence of wave operators for one-dimensional quantum walks
- Quantum time delay for unitary operators: general theory
- Weak limit theorem for a nonlinear quantum walk
- Strongly trapped space-inhomogeneous quantum walks in one dimension
- Asymptotic properties of generalized eigenfunctions for multi-dimensional quantum walks
- Spectral and scattering properties of quantum walks on homogenous trees of odd degree
- Two-dimensional quantum central limit theorem by quantum walks
- Index Theorems for One-dimensional Chirally Symmetric Quantum Walks with Asymptotically Periodic Parameters
- An eigenfunction expansion formula for one-dimensional two-state quantum walks
- A weak limit theorem for a class of long range type quantum walks in 1d
- Spectral analysis of three-state quantum walks with general coin matrices
- The Witten Index for One-dimensional Non-unitary Quantum Walks with Gapless Time-evolution
- Resonances in finitely perturbed quantum walks, resonance expansion and generic simplicity