In the model of diffusive transport, electrons repeatedly scatter with a scattering time $\tau$. After a scattering event, the electrons move in a random direction. Between scattering events, the electrons move under the influence of the applied electric and magnetic fields. In the simulation below, the blue dots represent electrons. The red dot is the average initial position of the electrons, and the green dot is the average position. Press the button to start the simulation again.

$y$ [μm]
	$x$ [μm]

time:  s, $θ_H=$  [rad]
$m=$  [kg], $q=$  [C], $dt=$  [s]
$B_{z}=$ 2 [T]
$E_x=$ 1E5 [V/m]
$E_y=$ 0 [V/m]
$τ_{sc}=$ 2 [s]

The parameters of the simulation can be adjusted with the sliders. There are buttons to start the simulation with certain preset conditions.

• - Sets the magnetic field to zero and the electric field to $10^{5}\text{ V/m}$ in the positive $x-$direction. The scattering time is set to be long so that it is unlikely that a scattering event will be observed during the simulation. The electrons accelerate in the negative $x-$direction following parabolic trajectories. The average electron velocity increases linearly with time.
• - Sets the magnetic field to zero and the electric field to $10^{5}\text{ V/m}$ in the positive $x-$direction. The scattering time is set to be short enough that there are many scattering events during the simulation. The electrons move in the negative $x-$direction with a constant average drift velocity.
• - Sets the magnetic field to zero and the electric field to zero. The scattering time is set to be short enough that there are many scattering events during the simulation. The electrons diffuse away from the origin.
• - Sets the magnetic field to 1 T and the electric field to zero. The scattering time is set to be long enough so that scattering events are rare. The electrons mostly move in circles.
• - Sets the magnetic field to 2 T and the electric field to $10^{5}\text{ V/m}$ in the positive $x-$direction. The scattering time is set to be long enough so that scattering events are rare. The electrons mostly follow prolate cycloid trajectories in a direction that is perpendicular to the electric field and the magnetic field.
• - Sets the magnetic field to 2 T and the electric field to $10^{5}\text{ V/m}$ in the positive $x-$direction. The scattering time is set to be short so that there are many scattering events during the simulation. The electrons follow prolate cycloid trajectories between the scattering events. The average velocity of the electrons is constant, and they move at an angle to the electric field. The Hall angle is between the electric field and the current density. The current density is in the opposite direction to the average electron motion.