Resolvent methods for quantum walks with an application to a Thue-Morse quantum walk. (English) Zbl 1470.81041
Summary: In this expository work, we discuss spatially inhomogeneous quantum walks in one dimension and describe a genre of mathematical methods that enables one to translate information about the time-independent eigenvalue equation for the unitary generator into dynamical estimates for the corresponding quantum walk. To illustrate the general methods, we show how to apply them to a 1D coined quantum walk whose coins are distributed according to an element of the Thue-Morse subshift.
MSC:
| 81S25 | Quantum stochastic calculus |
| 60G50 | Sums of independent random variables; random walks |
| 34L15 | Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators |
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