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 investigate realistic problems, due to the otherwise exorbitant execution-times and memory requirements. Because of the annihilation step, a straight-forward parallelization of the Wigner Monte Carlo code is not possible, since sub-ensembles of particles can not be treated independently. Moreover, the large memory requirements of the annihilation procedure presents challenges when working in a distributed-memory setting. A solution to this problem is presented here with a parallelization approach using a spatial domain decomposition, implemented using the message passing interface. The presented benchmark results, based on standard one-dimensional examples, exhibit a good efficiency in the scalability of not only speed, but also memory consumption, which is paramount for the simulation of realistic devices.

We present a Wigner signed particles analysis of the lense‐governed electron state dynamics based on the quantitative theory of coherence reformulated in phase space terms. Electrostatic lenses are used for manipulating electron evolution and are therefore attractive for applications in novel engineering disciplines like entangletronics. The signed particle model of Wigner evolution enables physically intuitive insights into the processes maintaining coherence. Both, coherent processes and scattering‐caused transitions to classical dynamics are unified by a scattering‐aware particle model of the lense‐controlled state evolution. Our approach bridges the fairly new theory of coherence with the Wigner signed particle method.

We present a signed particle computational approach for the Wigner transport model and use it to analyze the electron state dynamics in quantum wires focusing on the effect of surface roughness. Usually surface roughness is considered as a scattering model, accounted for by the Fermi Golden Rule, which relies on approximations like statistical averaging and in the case of quantum wires incorporates quantum corrections based on the mode space approach. We provide a novel computational approach to enable physical analysis of these assumptions in terms of phase space and particles. Utilized is the signed particles model of Wigner evolution, which, besides providing a full quantum description of the electron dynamics, enables intuitive insights into the processes of tunneling, which govern the physical evolution. It is shown that the basic assumptions of the quantum-corrected scattering model correspond to the quantum behavior of the electron system. Of particular importance is the distribution of the density: Due to the quantum confinement, electrons are kept away from the walls, which

An analysis of the possible formulations of the Wigner equation under a general gauge for the electric field is presented with an emphasis on the computational aspects of the problem. The numerical peculiarities of those formulations enable alternative computational strategies based on existing numerical methods applied in the Wigner formalism, such as finite difference or stochastic particle methods. The phase space formulation of the problem along with certain relations to classical mechanics offers an insight about the role of the gauge transforms in quantum mechanics.

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