Non-Hermitian Hamiltonian approach to quantum transport in disordered networks with sinks: validity and effectiveness

Abstract

We investigate the validity of the non-Hermitian Hamiltonian approach in describing quantum transport in disordered tight-binding networks connected to external environments, acting as sinks. Usually, non-Hermitian terms are added, on a phenomenological basis, to such networks to summarize the effects of the coupling to the sinks. Here we consider a paradigmatic model of open quantum network for which we derive a non-Hermitian effective model, discussing its limit of validity by a comparison with the analysis of the full Hermitian model. Specifically, we consider a ring of sites connected to a central one-dimensional lead. The lead acts as a sink which absorbs the excitation initially present in the ring. The coupling strength to the lead controls the opening of the ring system. This model has been widely discussed in literature in the context of light-harvesting systems. We analyze the effectiveness of the non-Hermitian description both in absence and in presence of static disorder on the ring. In both cases, the non-Hermitian model is valid when the energy range determined by the eigenvalues of the ring Hamiltonian is smaller than the energy band in the lead. Under such condition, we show that results about the interplay of opening and disorder, previously obtained within the non-Hermitian Hamiltonian approach, remain valid when the full Hermitian model in presence of disorder is considered. The results of our analysis can be extended to generic networks with sinks, leading to the conclusion that the non-Hermitian approach is valid when the energy dependence of the coupling to the external environments is sufficiently smooth in the energy range spanned by the eigenstates of the network.

Final version, 20 pages, 15 figures

References in corpus (11)

• The physics of exceptional points
• Environment-Assisted Quantum Walks in Photosynthetic Energy Transfer
• Dephasing assisted transport: Quantum networks and biomolecules
• Highly efficient energy excitation transfer in light-harvesting complexes: The fundamental role of noise-assisted transport
• Efficiency of energy transfer in a light-harvesting system under quantum coherence
• Formation of long-lived, scarlike modes near avoided resonance crossings in optical microcavities
• Non-exponential and oscillatory decays in quantum mechanics
• Revisiting the Fermi Golden Rule: Quantum Dynamical Phase Transition as a Paradigm Shift
• Design principles and fundamental trade-offs in biomimetic light harvesting
• Cooperative robustness to dephasing: single-exciton Superradiance in a nanoscale ring to model natural light-harvesting systems
• Transport through quasi-one-dimensional wires with correlated disorder

Cited by in corpus (5)

• Opening-Assisted Coherent Transport in the Deep Classical Regime
• Optimal Dephasing for Ballistic Energy Transfer in Disordered Linear Chains
• Non-Hermitian and Zeno limit of quantum systems under rapid measurements
• Time reversal of a discrete system coupled to a continuum based on non-Hermitian flip
• Quantum transfer through small networks coupled to phonons: effects of topology vs phonons