calc_n_numba

static ThomasFermi.calc_n_numba(n_0, qV, K_mat, g_0, beta, mu, delta_x, rel_tol, abs_tol, coulomb_steps, use_n_guess, max_iterations, use_combination_method, g0_dx_K_plus_1_inv)

Calculates the particle density n(x) using numba.

This is done by by solving the set of self-consistent equations, eqs. (4) & (5) of arXiv:2509.13298 by using the successive iteration method.

Parameters:

  • n_0 (ndarray[float]) – Initial guess (in 1/nm) for the particle density n(x). Pass np.zeros(len(qV)) if no initial guess is desired.

  • qV (ndarray[float]) – The potential V(x) formed by the gates, multiplied by the particle charge q. (qV has units of meV).

  • K_mat (ndarray[float]) – 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].

  • g_0 (float) – Coefficient of the density of states (in 1/(meV*nm) for 2D).

  • beta (float) – The inverse temperature \(1/(k_B T)\) (in 1/meV).

  • mu (float) – The Fermi level (in meV).

  • delta_x – The spacing (in nm) between successive x-values.

  • rel_tol (float) – The relative tolerance to accept a solution. The calculation will terminate if the difference delta_n between successive iterations of n(x) is small enough that norm(delta_n)**2 < rel_tol**2 * norm(n) * norm(n_prev), or if the condition for abs_tol is satisfied.

  • abs_tol (float) – The absolute tolerance to accept a solution. The calculation will terminate if the difference delta_n between successive iterations of n(x) is small enough that norm(delta_n) * delta_x < abs_tol, or if the condition for rel_tol is satisfied.

  • coulomb_steps (int) – The number of steps over which to turn on the Coulomb interaction.

  • use_n_guess (bool) – If True, the Coulomb potential will be applied all at once. If false, it will be turned on slowly over a series of steps.

  • max_iterations (int) – The maximum number of iterations to perfom.

  • use_combination_method (bool) – Whether to use a combination of the previous 2 iterations when solving for n(x): n = (1 + g_0 * delta_x * K_mat)^-1 * (n + g_0 * delta_x * K_mat * n_prev)

  • g0_dx_K_plus_1_inv (ndarray[float]) – Inverse of (g_0 * delta_x * K_mat + identity).

Returns:

  • n (ndarray[float]) – The calculated particle density (in 1/nm).

  • phi (ndarray[float]) – The calculated value (in meV) of phi(x), given by np.dot(K_mat, n) * delta_x.

  • converged (bool) – Whether the process converged to the required tolerance within the specified number of iterations.