Proves explicit velocity upper bounds for periodic quantum walks including linear bottleneck effects for small transmission parameters and harmonic-mean bounds, plus a general lower bound.
Localization for Random Unitary Operators
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abstract
We consider unitary analogs of $1-$dimensional Anderson models on $l^2(\Z)$ defined by the product $U_\omega=D_\omega S$ where $S$ is a deterministic unitary and $D_\omega$ is a diagonal matrix of i.i.d. random phases. The operator $S$ is an absolutely continuous band matrix which depends on a parameter controlling the size of its off-diagonal elements. We prove that the spectrum of $U_\omega$ is pure point almost surely for all values of the parameter of $S$. We provide similar results for unitary operators defined on $l^2(\N)$ together with an application to orthogonal polynomials on the unit circle. We get almost sure localization for polynomials characterized by Verblunski coefficients of constant modulus and correlated random phases.
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math-ph 2years
2026 2verdicts
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Sufficient conditions are proven for zero velocity in position-dependent 1D quantum walks via an a priori velocity bound depending on sparse site sequences and local coin parameters, with extensions to random cases and CMV matrices.
citing papers explorer
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Bottleneck Effects and Harmonic-Type Velocity Bounds for Periodic Quantum Walks
Proves explicit velocity upper bounds for periodic quantum walks including linear bottleneck effects for small transmission parameters and harmonic-mean bounds, plus a general lower bound.
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Absence of Ballistic Transport in Quantum Walks with Asymptotically Reflecting Sites
Sufficient conditions are proven for zero velocity in position-dependent 1D quantum walks via an a priori velocity bound depending on sparse site sequences and local coin parameters, with extensions to random cases and CMV matrices.