We consider a stationary Schrödinger-Poisson system on a bounded interval of the real axis. The Schrödinger operator is defined on the bounded domain with transparent boundary conditions. This allows to model a non-zero current flow trough the boundary of the interval. We prove that the system always admits a solution and give explicit a priori estimates for the solutions.

We consider a one-dimensional coupled stationary Schrödinger drift-diffusion model for quantum semiconductor device simulations. The device domain is decomposed into a part with large quantum effects (quantum zone) and a part where quantum effects are negligible (classical zone). We give boundary conditions at the classicquantum interface which are current preserving. Collisions within the quantum zone are introduced via a Pauli master equation. To illustrate the validity we apply the model to three resonant tunneling diodes.

We deal with a stationary, dissipative Schrödinger–Poisson system which allows for a current flow through an open, spatially one-dimensional quantum system determined by a dissipative Schrödinger operator. This dissipative Schrödinger operator can be regarded as a pseudo-Hamiltonian of the corresponding open quantum system. The (self-adjoint) dilation of the dissipative operator serves as a quasi-Hamiltonian of the system which is used to define physical quantities such as density and current for the open quantum system. The thus defined charge density in its dependence on the electrostatic potential is the nonlinear term in Poisson’s equation. We prove that the dissipative Schrödinger–Poisson system always admits a solution and all solutions are included in a ball the radius of which depends only on the data of the problem.

No abstract

Non-self-adjoint operators play an important role in the modeling of open quantum systems. We consider a one-dimensional Schrödinger-type operator of the form −(1/2)(d/dx)(1/m)(d/dx)+V−∑κjδ(⋅−xj),  Im(κj)>0, with dissipative boundary conditions. An explicit description of the characteristic function, the minimal dilation and the generalized eigenfunctions of the dilation is given. The quantities of carrier and current densities are rigorously defined. Furthermore, we will show that the current is not constant and that the variation of the current depend essentially on the chosen density matrix and the imaginary parts of the delta potentials, i.e., Im(κj). This correspondence can be used to model a recombination-generation rate in the open quantum system.