Herein, an analysis of interference effects as a result of the electron evolution within a coherent transport medium is presented, offering a double-dopant Coulomb potential structure. Injection of coherent electron states into the structure is used to investigate the effects on the current transport behavior within the quantum Wigner phase space picture. Quantum effects are outlined by using classical simulation results as a reference frame. The utilized signed particle approach inherently provides a seamless transition between the classical and quantum domain. Based on this the occurring quantum effects caused by the non-locality of the action of the quantum potential, leading to spatial resonance, can be indentified. The resulting interference patterns enable novel applications in the area of entangletronics.Introduction: Correctly describing and predicting quantum effects in nanoelectronic devices remains a key challenge. An attractive way to do so is to compare quantum with classical effects, enabling to identify quantumness in the generated results. However, the transition from quantum to classical transport requires a principal change in the physical description.In contrast to classical processes comprised by elementary events associated with probabilities, the interplay of phases and amplitudes gives rise to interference effects which cannot be described as a cumulative sum of probabilities. A given quantum transport problem does not allow for a decomposition into separate sub-tasks as suggested by the Matthiessen rule of classical transport, and needs to be treated in its entirety.[1] Therefore, the interplay of seemingly simple processes, as for example electron evolution with Coulomb potentials, fundamentally differs when using a classical or a quantum description.

Gauge-invariant Wigner theories are formulated in terms of the kinetic momentum, which-being a physical quantity-is conserved after a change of the gauge. These theories rely on a transform of the density matrix, originally introduced by Stratonovich, which generalizes the Weyl transform by involving the vector potential. We thus present an alternative derivation of the Weyl-Stratonovich transform, which bridges the concepts and notions used by the different, available gauge-invariant approaches and thus links physically intuitive with formal mathematical viewpoints. Furthermore, an explicit form of the Wigner equation, suitable for numerical analysis and corresponding to general, inhomogeneous, and time-dependent electromagnetic conditions, is obtained. For a constant magnetic field, the equation reduces to two models: in the case of a constant electric field, this is the ballistic Boltzmann equation, where classical particles are driven by local forces. The second model, derived for general electrostatic conditions, involves novel physics, where the magnetic field acts locally via the Liouville operator, while the electrostatics is determined by the manifestly nonlocal Wigner potential. A significant consequence of our work is the fact that now the constant magnetic field case can be treated with existing numerical approaches developed for the standard, scalar potential Wigner theory. Therefore, in order to demonstrate the feasibility of the approach, a stochastic method is applied to simulate a physically intuitive evolution problem.

The interplay of coherence effects, like non-locality and tunneling, generates a quantum current density path around a repulsive dopant that is much more efficient than in the classical case.

The continued reduction of semiconductor device feature sizes towards the single-digit nanometer regime involves a variety of quantum effects. Modeling quantum effects in phase space in terms of the Wigner transport equation has evolved to be a very effective approach to describe such scaled down complex systems, accounting from full quantum processes to dissipation dominated transport regimes including transients. Here, we discuss the challanges, myths, and opportunities that arise in the study of these complex systems, and particularly the advantages of using phase space notions. The development of particle-based techniques for solving the transport equation and obtaining the Wigner function has led to efficient simulation approaches that couple well to the corresponding classical dynamics. One particular advantage is the ability to clearly illuminate the entanglement that can arise in the quantum system, thus allowing the direct observation of many quantum phenomena.