Efficient calculation of the two-dimensional Wigner potential

The solution of the two-dimensional (2D) Wigner equation has become numerically feasible in recent times, using the Monte Carlo method fortified with the notion of signed particles. The calculation of the Wigner potential (WP) in these 2D simulations consumes a considerable part of the computation time. A reduction of the latter is therefore very desirable, in particular, if self-consistent solutions are pursued, where the WP must be recalculated many times. An algorithm is introduced here - named box discrete Fourier transform (BDFT) - that reduces the computational effort roughly by a factor of five.