The excitation operator approach to non-Markovian dynamics of quantum impurity models in the Kondo regime

Abstract

We present a numerical method for studying the real time dynamics of a small interacting quantum system coupled to an infinite fermionic reservoir. By building an orthonormal basis in the operator space, we turn the Heisenberg equation of motion into a system of linear differential equations, which is then solved iteratively by constructing excitation operators. The application of our method depends on a layer structure in the operator space, which help us to turn an infinite linear system into a series of small systems. We apply the method to investigate the decoherence dynamics of quantum impurity models in the Kondo regime with a non-Markovian reservoir. Taking full account of environmental back-actions and electron-electron interactions, we find that the coexistence of the Kondo correlation and a non-Markovian reservoir induces coherence ringings, which will be suppressed by either driving the system away from the particle-hole symmetric point or changing the reservoir into a Markovian one.

7 pages, 5 figures

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• Effect of incommensurate disorder on the resonant tunneling through Majorana bound states on the topological superconductor chains
• The numerical operator method to the real time dynamics of currents through the nanostructures with different topologies