Paul Ellinghaus

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The solution of the Wigner equation, using the Monte Carlo method [1] along with the signed-particle technique [2], requires a finite coherence length to be chosen. We investigate how the choice of the coherence length influences computational aspects of the calculation of the Wigner potential, like momentum resolution. Additionally, the physical(More)
The Wigner Monte Carlo method, based on the generation and annihilation of particles, has emerged as a promising approach to treat transient problems of quantum electron transport in nanostructures. Tackling these simulations in multiple spatial dimensions demands a parallelized approach to facilitate a practical application of the method in order to(More)
The signed-particle Monte Carlo method for solving the Wigner equation has made multi-dimensional solutions numerically feasible. The latter is attributable to the concept of annihilation of independent indistinguishable particles, which counteracts the exponential growth in the number of particles due to generation. After the annihilation step, the(More)
The Wigner equation can conveniently describe quantum transport problems in terms of particles evolving in the phase space. Improvements in the particle generation scheme of the Wigner Monte Carlo method are shown, which increase the accuracy of simulations as validated by comparison to exact solutions of the Schrödinger equation. Simulations with a(More)
The Wigner formalism provides a convenient formulation of quantum mechanics in the phase space. Deterministic solutions of the Wigner equation are especially needed for problems where phase space quantities vary over several orders of magnitude and thus can not be resolved by the existing stochastic approaches. However, finite difference schemes have been(More)
Conducting Wigner Monte Carlo simulations remains highly challenging primarily due to the method’s critical annihilation step, required to counter-balance the continuous generation of particles to keep the simulation computationally feasible. The memory demands of the annihilation algorithm itself is proportional to the dimensionality and resolution of the(More)
Schur complement technique, an effective implementation of the weak Galerkin is developed a linear system involving unknowns only associated with element boundaries. In this talk, several numerical applications of weak Galerkin methods will be discussed. at extending the well-known DUNE framework for PDE simulations (see to prepare(More)
The solution of the two-dimensional (2D) Wigner equation has become numerically feasible in recent times, using the Monte Carlo method fortified with the notion of signed particles. The calculation of the Wigner potential (WP) in these 2D simulations consumes a considerable part of the computation time. A reduction of the latter is therefore very desirable,(More)
The Wigner Monte Carlo solver, using the signed-particle method, is based on the generation and annihilation of numerical particles. The memory demands of the annihilation algorithm can become exorbitant, if a high spatial resolution is used, because the entire discretized phase space is represented in memory. Two alternative algorithms, which greatly(More)
The contact regions in nanoscaled transistors play an increasingly important role in the overall performance of the devices. An electrostatic lens in the source contact region to focus a beam of electron wave packets into a nanoscaled channel is investigated here, using a Wigner Ensemble Monte Carlo simulator. An improvement in the drive-current is achieved(More)