Fig. 3.5 Evolution of the Probability density distribution at different times for different values of
the external Force F: The initial Gaussian distribution, P (x, 0) = (2π 1/2 σ ) −1 exp
(x−x 0 )
2 1/2 σ
2
is
plotted. We can observe even with F = 0. The probability density evolves to the left, meaning that
the current is to the left because the potential is slightly tilded to the right, in accordance to Fig. 3.4.
Simulation performed with Program 3.2, with the parameters: D = 5 × 10 −4 , V 0 = 1.0, V ( ˜
x) =
1
2π
sin (2π ˜
x) −
1
4 sin (4π ˜
x)
the external Force F: The initial Gaussian distribution, P (x, 0) = (2π 1/2 σ ) −1 exp
(x−x 0 )
2 1/2 σ
2
is
plotted. We can observe even with F = 0. The probability density evolves to the left, meaning that
the current is to the left because the potential is slightly tilded to the right, in accordance to Fig. 3.4.
Simulation performed with Program 3.2, with the parameters: D = 5 × 10 −4 , V 0 = 1.0, V ( ˜
x) =
1
2π
sin (2π ˜
x) −
1
4 sin (4π ˜
x)