Quantum master equation for electron transport through quantum dots and single molecules

By U. Harbola, Massimiliano Esposito, Shaul Mukamel. 2006

190 citations recorded by the source corpus.

A quantum master equation QME is derived for the many-body density matrix of an open current-carrying system weakly-coupled to two metal leads. The dynamics and the steady-state properties of the system for arbitrary bias are studied using projection operator techniques, which keep track of the number of electrons in the system. We show that coherences between system states with different number of electrons, n Fock space coherences, do not contribute to the transport to second order in system-lead coupling. However, coherences between states with the same n may effect transport properties when the damping rate is of the order of or faster than the system Bohr frequencies. For large bias, when all the system many-body states lie between the chemical potentials of the two leads, we recover previous results. In the rotating wave approximation when the damping is slow compared to the Bohr frequencies, the dynamics of populations and coherences in the system eigenbasis are decoupled. The QME then reduces to a birth and death master equation for populations.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/3a5f91e7f3d6d1e495d34de89ff904a1d7595a99

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

In Electrical and Electronic Engineering

Citations in the corpus

Markovian master equations for quantum thermal machines: local versus global approach (2017, background): “[11] shows that the global approach neglects terms that influence the current through a two-terminal electric conductor.”
Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems (2008, methodology): “(130) is extended to infinity), we perform the RWA approximation which is equivalent to assume that the lead correlation functions are diagonal in s [88].”
Nonequilibrium physics in biology (2019, background): “5 (d)) (Harbola et al., 2006; Zhang and Wang, 2014, 2015c, 2016).”
Dynamics of non-Markovian open quantum systems (2015, background): “…theory of OQSs, including rate equations (Gurvitz and Prager, 1996), master and Fokker-Planck equations (Büsser et al., 2014; Ghosh et al., 2012; Harbola et al., 2006; Li et al., 2005; Pedersen and Wacker, 2005; Timm, 2008), stochastic Schrödinger equations (Zhao et al., 2012), or path…”