Many-particle density-matrix approach to a quantum dot system for the strong electron accumulation case

We consider the system of an electronic quantum dot with a base set of discrete single-particle levels due to quantization effects in an arbitrarily given attractive potential. Intradot electron-electron interaction is described employing the full many-particle Coulomb interaction Hamiltonian in second quantization. Interaction effects arising from a capacitive response of the environment is incorporated within the framework of a classical interaction term. Hereby the environment consists of thermodynamical electron reservoirs coupled to the quantum dot system via weak tunnel barriers. Using this quantum dot model Hamiltonian we present a many-particle density-matrix approach in order to describe the thermodynamical state of the many-electron system and calculate expectation values of observables such as particle number and total spin. In the following we assume that exactly one reservoir dominates concerning a very weak particle injection. The other reservoirs are thought of as negligible tunneling probes. Especially the system of a laterally confined sub-$\mu \mathrm{m}$ resonant tunneling diode in the single-electron tunneling regime for the case of strong barrier asymmetry will be discussed as an example. Numerical results for realistic diode parameters suggest the definition of a capacitive and atomic regime of such an interacting quantum dot system.