4 papers
Ergodicity in discrete-time quantum walks
Kiran Kumar, Mostafa Sabri
We undertake a detailed analysis of ergodicity for homogeneous discrete-time quantum walks on the integer lattice. The most significant result of our paper holds in dimension one,…
Limiting distributions of ergodic continuous-time quantum walks on periodic graphs
Anne Boutet de Monvel, Kiran Kumar A. S., Mostafa Sabri
In this expository note, we study several families of periodic graphs which satisfy a sufficient condition for the ergodicity of the associated continuous-time quantum walk. For th…
The curious spectra and dynamics of non-locally finite crystals
Joachim Kerner, Olaf Post, Mostafa Sabri +1
This paper is devoted to the investigation of the spectral theory and dynamical properties of periodic graphs which are not locally finite but carry non-negative, symmetric and sum…
Ergodic theorems for continuous-time quantum walks on crystal lattices and the torus
Anne Boutet de Monvel, Mostafa Sabri
We give several quantum dynamical analogs of the classical Kronecker-Weyl theorem, which says that the trajectory of free motion on the torus along almost every direction tends to…