The Wigner function was formulated in 1932 by Eugene Paul Wigner, at a time when quantum mechanics was in its infancy. In doing so, he brought phase space representations into quantum mechanics. However, its unique nature also made it very interesting for classical approaches and for identifying the deviations from classical behavior and the entanglement that can occur in quantum systems. What stands out, though, is the feature to experimentally reconstruct the Wigner function, which provides far more information on the system than can be obtained by any other quantum approach. This feature is particularly important for the field of quantum information processing and quantum physics. However, the Wigner function finds wide-ranging use cases in other dominant and highly active fields as well, such as in quantum electronics—to model the electron transport, in quantum chemistry—to calculate the static and dynamical properties of many-body quantum systems, and in signal processing—to investigate waves passing through certain media. What is peculiar in recent years is a strong increase in applying it: Although originally formulated 86 years ago, only today the full potential of the Wigner function—both in ability and diversity—begins to surface. This review, as well as a growing, dedicated Wigner community, is a testament to this development and gives a broad and concise overview of recent advancements in different fields.

Connecting circuit layers with nanowires and nanotransistors may bring about a paradigm shift in microchip design.

The room-temperature velocity-field characteristics for $n$ -type gallium nitride and $\mathrm{Al}\mathrm{Ga}\mathrm{N}∕\mathrm{Ga}\mathrm{N}$ heterostructures, grown epitaxially on sapphire, were determined experimentally. A pulsed voltage input and four-point measurements were used on special geometry samples to determine the electron drift velocity as a function of applied electric field in the basal plane. These measurements show apparent saturation velocities near $2.5\times {10}^7\mathrm{cm}∕\mathrm{s}$ at $180\mathrm{kV}∕\mathrm{cm}$ for the $n$ -type gallium nitride and $3.1\times {10}^7\mathrm{cm}∕\mathrm{s}$ at $140\mathrm{kV}∕\mathrm{cm}$ for the $\mathrm{Al}\mathrm{Ga}\mathrm{N}∕\mathrm{Ga}\mathrm{N}$ heterostructures. A comparison of these studies shows that the experimental velocities are close to previously published simulations based upon Monte Carlo techniques.

In this report, we review the results of our joint experimental and theoretical studies of electron-interference, and interaction, phenomena in open electron cavities known as quantum dots. The transport through these structures is shown to be heavily influenced by the remnants of their discrete density of states, elements of which remain resolved in spite of the strong coupling that exists between the cavity and its reservoirs. The experimental signatures of this density of states are discussed at length in this report, and are shown to be related to characteristic wavefunction scarring, involving a small number of classical orbits. A semiclassical analysis of this behaviour shows it to be related to the effect of dynamical tunnelling, in which electrons are injected into the dot tunnel through classically forbidden regions of phase space, to access isolated regular orbits. The dynamical tunnelling gives rise to the formation of long-lived quasi-bound states in the open dots, and the many-body implications associated with electron charging at these resonances are also explored in this report.