Higher-Order Kinetic Expansion of Quantum Dissipative Dynamics: Mapping Quantum Networks to Kinetic Networks

TL;DR

This paper introduces a higher-order quantum kinetic expansion (QKE) formalism to accurately model dissipative dynamics in quantum networks, capturing multi-site coherence and bath effects, and distinguishing quantum phenomena like tunneling and interference.

Contribution

It develops a systematic higher-order QKE framework that extends beyond NIBA, enabling detailed analysis of quantum coherence effects in dissipative systems.

Findings

Higher-order QKE accurately predicts quantum dissipative dynamics.

The formalism distinguishes quantum tunneling and interference effects.

Analytical rate kernels derived for quantum harmonic baths.

Abstract

We apply a new formalism to derive the higher-order quantum kinetic expansion (QKE) for studying dissipative dynamics in a general quantum network coupled with an arbitrary thermal bath. The dynamics of system population is described by a time-convoluted kinetic equation, where the time-nonlocal rate kernel is systematically expanded on the order of off-diagonal elements of the system Hamiltonian. In the second order, the rate kernel recovers the expression of the noninteracting-blip approximation (NIBA) method. The higher-order corrections in the rate kernel account for the effects of the multi-site quantum coherence and the bath relaxation. In a quantum harmonic bath, the rate kernels of different orders are analytically derived. As demonstrated by four examples, the higher-order QKE can reliably predict quantum dissipative dynamics, comparing well with the hierarchic equation approach. More importantly, the higher-order rate kernels can distinguish and quantify distinct nontrivial quantum coherent effects, such as long-range energy transfer from quantum tunneling and quantum interference arising from the phase accumulation of interactions.