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

Abstract

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 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 or faster then 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 of the system), the dynamics of populations and the coherences in the system eigenbasis are decoupled. The QME then reduces to a birth and death master equation for populations.

Interference effects in the counting statistics of electron transfers through a double quantum dot

“…38 decouples the coherence and population part of the system density matrix in the Liouville space eliminating all interferences. For model A, the RWA applied to Eq.…”

“…38 Liouville space allows a compact superoperator notation. We define the following Liouville space superoperators:…”

A Perturbative Method for Nonequilibrium Steady State of Open Quantum Systems

“…Then, we have an O(v) correction toρ SA ss , which gives a perturbative solution of Eq. (17). This perturbation theory is valid up to the first order in v, which is the same order as that in the QME (3).…”

“…In quantum systems, one of the theoretical frameworks widely used for open systems is the quantum master equation (QME) [1], an equation of motion for the density matrix of the system. In fact, the QME is used in various fields of physics: e.g., quantum optics [1,2], nuclear magnetic resonance [3], electron transfer in chemical physics and biophysics [4,5], heat transport [6,7,8,9,10,11,12,13,14], electronic transport in mesoscopic conductors [15,16,17,18,19], spin transport [20], and nonequilibrium thermodynamics and statistical physics [21,22,23,24,25]. Therefore, the QME is a reliable approach to investigating NESS in various systems (c.f.…”

Time-dependent density functional theory for quantum transport

“…The simulation of transient current has also been attempted by manybody quantum master equation approaches. [24][25][26][27][28] Yan and coworkers have started from a master equation based second-order quantum dissipation theory (QDT), and derived an EOM for the RSDM within TDDFT framework, 8 where the bulk electrodes are treated as electron reservoirs. This was followed by the recent establishment of a formally exact QDT for the dynamics of an arbitrary non-Markovian dissipative systems interacting with bath surroundings.…”