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One-Dimensional (1D) Wigner Simulation Results: a wave packet interacting with a potential barrier.


These two videos shows an electron wave packet interacting with a potential barrier. Once the packet reaches the barrier, reflection and tunneling phenomena start to appear. The calculations are obtained by using the Wigner Monte Carlo method, a powerful approach to solve the Wigner equation.



Two-Dimensional (2D) Wigner Simulation Results: a wave packet interacting with a potential wall.


The first video (left) shows the time-dependent evolution of a two-dimensional Gaussian wave packet interacting with a potential wall (depicted by a straight line). Once the packet reaches the wall, reflection and partial tunneling phenomena start to appear. The second video (right) shows the time-dependent evolution of a two-dimensional Gaussian wave packet interacting with a potential wall. The top left plot shows the classical evolution (Boltzmann), the other three plots shows the quantum evolution of the wave packet with different potential values. As expected, the higher the wall the closer to the classical dynamics.



Three-Dimensional (3D) Wigner-Boltzmann Simulation Results: a wave packet evolving in a single dopant system.


These videos show the time-dependent evolution of a three-dimensional (3D) Gaussian wave packet interacting with the potential due to a Phosphorus dopant atom in a Silicon device. The lattice temperature is (left) 20mK (ballistic regime) and (right) 300K (room temperature). This device represents a candidate for quantum computers based on Silicon.



Two-Dimensional (2D) Wigner Simulations: an electron wave packet in the presence of ordered and disordered arrays of dopants.


The first video (left) shows the time dependent evolution of an electron wave packet interacting in a ordered array of ionizied dopants (Phosphorus) embedded in Silicon. A symmetry is developed during the evolution. The second plot (right) shows the same situation in the case of a disordered array of dopants. The symmetry is now broken.



Wigner Solotronics: an electron wave packet in the presence of dopant honeycomb structures.


The first video (left) shows the time dependent evolution of an electron wave packet interacting in a planar phosphorus honeycomb structure. The devices behaves as a nanometer scaled wire. The second plot (right) shows the same situation in the presence of a added boron atom in the middle of the domain (scattering center). The device behaves as a resistor.

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(C) 2012-2017, Jean Michel Sellier.