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In the quest for signatures of coherent energy transfer we consider the trapping of excitations within the continuous-time quantum walk (CTQW) framework. The dynamics takes place on a discrete network of N sites. Out of the N sites we assume M sites to be traps and incorporate those phenomenologically into the CTQW formalism by a trapping operator, which leads to a new, non-hermitian Hamiltonian H = H0 + iÃ. The average CTQW survival probability Ð(t) for an excitation not to be trapped after some time t follows from the transition probabilities. For small numbers of traps, we show that Ð(t) displays different decay domains, related to distinct regions of the (imaginary part of the) spectrum of the Hamiltonian. In the limit of asymptotically large times, this leads in most cases to a simple exponential decay. However, this is not the case at intermediate, experimentally relevant times. We exemplify our analysis with, first, a linear system of N sites, with long-range interaction, and with traps at each end. In this case the decay at intermediate times obeys a power-law, which strongly differs from the corresponding classical exponential decay found in incoherent continuous-time random walk (CTRW) situations. Furthermore, we show that the introduction of long-range interactions leads for CTQW to slowing-down of the trapping processes, which is the opposite of what happens for CTRW. An explanation within a perturbation theoretical treatment will be given. References: [1] Phys. Rev. Lett. 100, 090601 (2007) [2] Phys. Rev. E 78, 021115 (2008) |
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