A New Optimized Adaptive Approach for Estimation of the Wigner Kernel

In this paper we study numerically an optimized Adaptive Monte Carlo algorithm for the Wigner kernel - an important problem in quantum mechanics represented by difficult multidimensional integrals. We will show the advantages of the optimized Adaptive MC algorithm and compare the results with the Adaptive approach from our previous work [4] and other stochastic approaches for computing the Wigner kernel in 3,6,9dimensional case. The 12-dimensional case will be considered for the first time. A comprehensive study and an analysis of the computational complexity of the optimized Adaptive MC algorithm under consideration has also been presented.