| Abstract: | Using the non-Hermitian Hamiltonians we consider the dynamics of two systems. (I) measurement of superconducting phase qubit states by tunneling into their continuum; the relations to the complex geometrical phases and artificial monopoles; the influence of the thermal reservoir. We compare this approach with other theoretical approaches and with the available experimental results. (II) Superradiance transition in photosynthetic light-harvesting complexes. In this part, we investigate the role of long-lasting quantum coherence in the efficiency of energy transport at room temperature in Fenna-Matthews-Olson photosynthetic complexes. The excitation energy transfer due to coupling of the light harvesting complex to the reaction center (“sink”) is analyzed. We show that, as the coupling to the reaction center is varied, maximal efficiency in energy transport is achieved in the vicinity of the superradiance transition, characterized by a segregation of the imaginary parts of the eigenvalues of the effective non-Hermitian Hamiltonian. Our results demonstrate that the presence of the sink (which provides a quasi-continuum in the energy spectrum) is the dominant effect in the energy transfer which takes place even in the absence of a thermal bath. This approach allows one to study the effects of finite temperature and the effects of any coupling scheme to the reaction center. Moreover, taking into account a realistic electric dipole interaction, we show that the optimal distance from the reaction center to the Fenna-Matthews-Olson system occurs at the superradiance transition, and we show that this is consistent with available experimental data. |
