calc_K_mat

qdflow.physics.simulation.calc_K_mat(x, K_0, sigma)

Calculates the Coulomb interaction matrix.

Specifically, it returns a Coulomb interaction strength given by:

\(K(x_1, x_2) = \frac{K_0}{\sqrt{(x_1-x_2)^2 + \sigma^2}}\).

Parameters:

• x (ndarray[float]) – A 1D array containing the x-values (in nm) used in the simulation. These values should be evenly spaced, e.g., use x = np.linspace(x_min, x_max, num_points).

• K_0 (float) – The electron-electron Coulomb interaction strength (in meV * nm).

• sigma (float) – A softening parameter (in nm) for the el-el Coulomb interaction used to avoid divergence when \(x_1 = x_2\). sigma should be on the scale of the width of the nanowire.

Returns:

K_mat – A 2D array, with shape (len(x), len(x)), where K_mat[i, j] gives the value of the Coulomb interaction (in meV) between two particles at points x[i] and x[j].

Return type:

ndarray[float]