Tunneling through molecules and quantum dots: Master-equation approaches
By C. Timm. 2008
169 citations recorded by the source corpus.
An important class of approaches to the description of electronic transport through molecules and quantum dots is based on the master equation. We discuss various formalisms for deriving a master equation and their interrelations. It is shown that the master equation derived by K\"onig et al. [Phys. Rev. Lett. 76, 1715 (1996); Phys. Rev. B 54, 16820 (1996)] is equivalent to the Wangsness-Bloch-Redfield master equation. The roles of the large-reservoir and Markov approximations are clarified. At low temperatures, when the quasiparticle lifetime becomes large, the Markov approximation can be derived from the assumption of weak tunneling under certain conditions. Interactions in the leads are shown to be irrelevant for the transport in the case of momentum-independent tunneling. It is explained why the $T$-matrix formalism gives incomplete results except for diagonal density operators to second order in the tunneling amplitudes. The time-convolutionless master equation is adapted to tunneling problems and a diagrammatic scheme for generating arbitrary orders in the tunneling amplitudes is developed.
Subfields: Atomic and Molecular Physics, and Optics, Electrical and Electronic Engineering
View Paper: https://www.semanticscholar.org/paper/7c6587bfd175247f3a4b3b16ff9204f8778e9f4e
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In Atomic and Molecular Physics, and Optics
In Electrical and Electronic Engineering
Citations in the corpus
- Spin excitations and correlations in scanning tunneling spectroscopy (2015, methodology): “In such a framework, coherent state superpositions could be accounted for by using, for example, a Bloch-Redfield approach in which the spin system is coupled to an open quantum-system [128, 114, 129] and in which interactions up to third order are included to account not only for the decay but also”
- Dynamics of non-Markovian open quantum systems (2015, background): “…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 integrals (Tu and Zhang, 2008a) [see also (Brandes, 2005) for a review].”