Spectral Stability of Unitary Network Models
arXiv:1502.02301 · doi:10.1142/S0129055X15300046
Abstract
We review various unitary network models used in quantum computing, spectral analysis or condensed matter physics and establish relationships between them. We show that symmetric one dimensional quantum walks are universal, as are CMV matrices. We prove spectral stability and propagation properties for general asymptotically uniform models by means of unitary Mourre theory.
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Cited by in corpus (21)
- Quantum walks with an anisotropic coin I: spectral theory
- Quantum walks with an anisotropic coin II: scattering 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
- Topological boundary invariants for Floquet systems and quantum walks
- Singular continuous Cantor spectrum for magnetic quantum walks
- Weak limit theorem for a one-dimensional split-step quantum walk
- A Constructive Approach to Topological Invariants for One-dimensional Strictly Local Operators
- Generalized eigenfunctions for quantum walks via path counting approach
- Thermalization of Fermionic Quantum Walkers
- On Fermionic walkers interacting with a correlated structured environment
- Fermionic walkers driven out of equilibrium
- Spectral and scattering properties of quantum walks on homogenous trees of odd degree
- Lower Bounds on the Localisation Length of Balanced Random Quantum Walks
- Engineering stable quantum currents at bulk boundaries
- Index Theorems for One-dimensional Chirally Symmetric Quantum Walks with Asymptotically Periodic Parameters
- On absolutely continuous spectrum for one-channel unitary operators
- Dynamical Localization and Transport properties of Quantum Walks on the hexagonal lattice
- Chirality induced Interface Currents in the Chalker Coddington Model
- Examples for stable quantum currents
- A weak limit theorem for a class of long range type quantum walks in 1d