Abstract
The present work studies the behaviour of continuous time quantum walks on regular hyperbranched fractals, whose centre is a trap. We focus on the variations of the eigenvalue spectrum of the transfer operator by tuning the trap strength from zero to infinity. We show that the degenerate eigenvalues are independent from the trap strength and can be obtained analytically. Due to this the mean survival probability is just in the intermediate range affected by the trap strength; moreover, because of the presence of real eigenvalues, the asymptotical probability of being outside the trap is not zero.
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