We consider two modifications of a recently proposed three-terminal quantum dot heat engine. First, we investigate the necessity of the thermalization assumption, namely that electrons are always thermalized by inelastic processes when traveling across the cavity where the heat is supplied. Second, we analyze various arrangements of tunneling-coupled quantum dots in order to implement a transmission function that is superior to the Lorentzian transmission function of a single quantum dot. We show that the maximum power of the heat engine can be improved by about a factor of two, even for a small number of dots, by choosing an optimal structure.

The finite-temperature transport properties of the spinless interacting fermion model coupled to noninteracting leads are investigated. Employing the unrestricted time-dependent Hartree-Fock (HF) approximation, the transmission probability and the nonlinear I-V characteristics are calculated, and compared with available analytical results and with numerical data obtained from a Hubbard-Stratonovich decoupling of the interaction. In the weak interaction regime, the HF approximation reproduces the gross features of the exact I-V characteristics but fails to account for subtle properties like the particular power law for the reflected current in the interacting resonant level model. Model and methods Spinless fermion modelWe consider a one-dimensional model of spinless fermions, where N C central sites (the molecule) with nearestneighbor interaction U are coupled to a left and a right lead of N L and N R non-interacting sites. The hopping parameter t 0 is, for simplicity, chosen to be the same in the leads and within the molecule, while the coupling between the leads and the molecule is described by a hopping parameter t′ and a nearest-neighbor interaction U′. The Hamiltonian reads

We consider a model of interacting spinless fermions coupled to non-interacting leads. Initially a non-equilibrium situation is imposed by applying a bias voltage and temper- ature gradient across the system. The time-evolution of the density matrix leads to a quasi-stationary state from which charge and energy currents can be extracted. Numeri- cal results based on the time-dependent Hartree-Fock approximation are compared with exact currents obtained from discrete Hubbard-Stratonovich decoupling of the interac- tion for small systems. For a wide range of parameters the time-evolution of the currents is reasonably well described within the Hartree-Fock approach.