calc_WKB_prob

static ThomasFermi.calc_WKB_prob(physics, qV_TF, islands, barriers, is_short_circuit)

Calculates the transition rates between islands.

For each barrier, this function calculates the WKB probability of transmission through the barrier and multiplies that by the average attempt rate of the islands on either side. If there is only one adjacent island (this happens for the leftmost and rightmost barriers), then the attempt rate for that one island is used.

The attempt rate is a measure of how frequently an particle in the island collides with a given wall of the island and attempts to tunnel out, given by \(\frac{v_F}{2x_\text{isl}}\), where \(x_\text{isl}\) is the length of the island.

Parameters:

  • physics (PhysicsParameters) – The physical device parameters.

  • qV_TF (ndarray[float]) – The Thomas-Fermi potential (in meV).

  • islands (ndarray[int]) – An array with shape (num_islands, 2) giving the islands, where the islands[i] is a length-2 integer array: [begin_index, end_index + 1] giving the indeces of physics.x corresponding to the island.

  • barriers (ndarray[int]) – An array with shape (num_barriers, 2) giving the barriers, where barriers[i] is a length-2 integer array [begin_index, end_index + 1] giving the indeces of physics.x corresponding to the barrier.

  • is_short_circuit (bool) – True if n is above the cutoff threshold everywhere along the x-axis, False otherwise.

Returns:

  • p_WKB (ndarray[float]) – An array with length equal to the number of barriers, where each entry is the transition rate across the corresponding barrier. This is calculated by multiplying the transition probability by the rate at which particles collide with the barrier.

  • tranmission_coef (ndarray[float]) – An array with length equal to the number of barriers, where each entry is the transition probability across the corresponding barrier.