Clemens Etl Dipl.-Ing. Publications

Biography Clemens Etl was born in Wr. Neustadt, Austria, in 1990. He studied Technical Mathematics at the TU Wien where he received his master's degree in 2019. After graduation, he worked as a scientific assistant in the field of artificial intelligence at the Know-Center in Graz. He joined the Institute for Microelectronics in May 2022 where he is currently working on his doctoral degree. He is researching high performance electron quantum transport modeling and simulation approaches.

Studying single electron dynamics in the presence of electromagnetic fields is particularly relevant for electron quantum optics. The ability to manipulate and control electron behavior at the quantum level is crucial for developing novel nanoscale electronic quantum devices.

A particularly suitable modeling approach is based on the Wigner function. Applying the Weyl-Stratonovich transform on the evolution equation yields the gauge-invariant Wigner equation, introducing the Wigner function f_W, representing the electron's state in the phase space.

However, This equation is highly complex and multidimensional, making it challenging to simulate. Thus, simplifying assumptions have to be made. The setting of an electron in a two-dimensional (2D) plane and assuming a linear magnetic field reduces the equation to two operators applied to the Wigner function: The Liouville and the quantum magnetic operator. While the Liouville operator leads to the classical evolution of the electron, the latter causes quantum effects, which can be seen in the signed-particle algorithm, where the particles represent the Wigner function. The particles evolve according to the Liouville operator like classical electrons would evolve in the given magnetic field. Their trajectory is interrupted by instantaneous scattering caused by the quantum magnetic operator, which leads to the generation of new particles. These particles then evolve like their parent particles with an offset in the phase space.

In Fig. 1, a simulated so-called snake state type of evolution of an electron can be seen. In this case, the electron oscillates around the y-axis, where the magnetic field is zero. The change in the magnetic field's orientation causes a change in the electron's rotation. This leads to an S-shaped trajectory, as the name snake state suggests. The evolution of the difference in the density between the quantum evolution, i.e., scattering is turned on, and the classical evolution, i.e., scattering is turned off, shows a redistribution of the density from the electron's center to the peripheral part caused by the quantum magnetic operator. Remarkably, the centers of both cases align with each other, per the Ehrenfest theorem.

Fig. 1: Simulated electron density of a snake state evolution: Difference between quantum and classical evolution. The dashed line shows the trajectory of the packet's center.