A quantum-mechanical compact model of the threshold voltage (VT) for quantum nanowire MOSFETs has been developed. This approach is based on analytical solutions for the decoupled 2D Schrödinger and 1D Poisson equations solved in the silicon channel. A quantum correction based on the perturbation theory has been also introduced to improve the model accuracy. Finally, the validity of the model ha...

In this paper we analyze the asymptotic behaviour of solutions to the Schrödinger– Poisson–Slater (SPS) system in the frame of semiconductor modeling. Depending on the potential energy and on the physical constants associated with the model, the repulsive SPS system develops stationary or periodic solutions. These solutions preserve the L(R) norm or exhibit dispersion properties. In comparison ...

The stationary one dimensional Schrödinger–Poisson system on a bounded interval is considered in the limit of a small Debye length (or small temperature). Electrons are supposed to be in a mixed state with the Boltzmann statistics. Using various reformulations of the system as convex minimization problems, we show that only the first energy level is asymptotically occupied. The electrostatic po...

The existence of positive solutions to Schrödinger–Poisson type systems in R 3 with critically growing nonlocal term is proved by using variational method which does not require usual compactness conditions. A key ingredient of the proof is a new Brézis–Lieb type convergence result.

The soliton structure of a gauge theory proposed to describe chiral excitations in the multi-Layer Fractional Quantum Hall Effect is investigated. A new type of derivative multi-component nonlinear Schrödinger equation emerges as effective description of the system that supports novel chiral solitons. We discuss the classical properties of the solutions and study relations to integrable systems.

In this paper, we introduce and study a convoluted version of the time fractional Poisson process by taking discrete convolution with respect to space variable in system differential equations that governs its state probabilities. We call introduced as (CFPP). The explicit expression for Laplace transform probabilities are obtained whose inversion yields one-dimensional distribution. Some stati...