| Recently, the dynamics of excitations in, e.g., ultra-cold Rydberg gases or in light-harvesting complexes, both of which can be modelled by networks, have been of particular interest. Here, the initial excitation (a Frenkel exciton) is created by absorbing a laser excitation or by capturing solar photons. The exciton is transported over the network until it encounters sites where it can get absorbed (the reaction center in the light-harvesting complexes). This process can be modelled by non-hermitian Hamiltonians having complex eigenvalues [1]. In the following, we study (ensemble-averaged) random networks in which the excitation can vanish only at certain (trap) nodes and investigate the survival probability that the exciton does not get trapped during the (quantum) walk over the network. We further show how this is related to the distribution of the imaginary parts of the eigenvalues of the Hamiltonian [2]. [1] O. Mülken, A. Blumen, Phys. Rep. 502, 37 (2011). [2] A. Anishchenko, A. Blumen, O. Mülken, in preparation. |
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