A pseudo-unitary quasiperiodic quantum walk model exhibits a novel mobility edge sharply dividing metallic and insulating phases plus a second transition unique to discrete time, with PT-symmetry breaking quantified by spectral winding number.
Dynamical Localization for d-Dimensional Random Quantum Walks
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abstract
We consider a d-dimensional random quantum walk with site-dependent random coin operators. The corresponding transition coefficients are characterized by deterministic amplitudes times independent identically distributed site-dependent random phases. When the deterministic transition amplitudes are close enough to those of a quantum walk which forbids propagation, we prove that dynamical localization holds for almost all random phases. This instance of Anderson localization implies that all quantum mechanical moments of the position operator are uniformly bounded in time and that spectral localization holds, almost surely.
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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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Mobility edges in pseudo-unitary quasiperiodic quantum walks
A pseudo-unitary quasiperiodic quantum walk model exhibits a novel mobility edge sharply dividing metallic and insulating phases plus a second transition unique to discrete time, with PT-symmetry breaking quantified by spectral winding number.
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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.