2010/11/10 by Carsten Timm
Computer Science · Mathematics · Physics and Astronomy · #Generator (circuit theory) #Lindblad equation #Markov chain #Master equation #Mathematical physics #Mathematics #Order (exchange) #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum and electron transport phenomena #Quantum master equation #Quantum mechanics #Statistical physics #cond-mat.mes-hall #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevb.83.115416
13 pages + appendices
arxiv created 2010/11/10 · openalex publication_date 2011/03/10 · arxiv updated 2013/05/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The master equation describing the nonequilibrium dynamics of a quantum dot coupled to metallic leads is considered. Employing a superoperator approach, we derive an exact time-convolutionless master equation for the probabilities of dot states, i.e., a time-convolutionless Pauli master equation. The generator of this master equation is derived order by order in the hybridization between dot and leads. Although the generator turns out to be closely related to the T-matrix expressions for the transition rates, which are plagued by divergences, in the time-convolutionless generator all divergences cancel order by order. The time-convolutionless and T-matrix master equations are contrasted to the Nakajima-Zwanzig version. The absence of divergences in the Nakajima-Zwanzig master equation due to the nonexistence of secular reducible contributions becomes rather transparent in our approach, which explicitly projects out these contributions. We also show that the time-convolutionless generator contains the generator of the Nakajima-Zwanzig master equation in the Markov approximation plus corrections, which we make explicit. Furthermore, it is shown that the stationary solutions of the time-convolutionless and the Nakajima-Zwanzig master equations are identical. However, this identity neither extends to perturbative expansions truncated at finite order nor to dynamical solutions. We discuss the conditions under which the Nakajima-Zwanzig-Markov master equation nevertheless yields good results.