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.
Propagation and spectral properties of quantum walks in electric fields
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abstract
We study one-dimensional quantum walks in a homogeneous electric field. The field is given by a phase which depends linearly on position and is applied after each step. The long time propagation properties of this system, such as revivals, ballistic expansion and Anderson localization, depend very sensitively on the value of the electric field $\Phi$, e.g., on whether $\Phi/(2\pi)$ is rational or irrational. We relate these properties to the continued fraction expansion of the field. When the field is given only with finite accuracy, the beginning of the expansion allows analogous conclusions about the behavior on finite time scales.
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math-ph 2years
2026 2verdicts
UNVERDICTED 2roles
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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.
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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.