Citation: Proceedings of the 2020 Federated Conference on Computer Science and Information Systems, M. Ganzha, L. Maciaszek, M. Paprzycki (eds). ACSIS, Vol. 21, pages 341–344 (2020)
Abstract. 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  and other stochastic approaches for computing the Wigner kernel in 3,6,9-dimensional 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.
- Berntsen J., Espelid T.O., Genz A. (1991) An adaptive algorithm for the approximate calculation of multiple integrals, ACM Trans. Math. Softw. 17: 437–451, https://doi.org/10.1145/210232.210233.
- Feynman R.P. (1948) Space-time approach to nonrelativistic quantum mechanics, Rev. Mod. Phys. 20, https://doi.org/10.1103/RevModPhys.20.367.
- Sellier J.M., Nedjalkov M., Dimov I. (2015) An introduction to applied quantum mechanics in the Wigner Monte Carlo formalism, Physics Reports Volume 577: 1–34, https://doi.org/10.1016/j.physrep.2015.03.001.
- Todorov, V., Dimov, I., Georgieva, R., & Dimitrov, S. Adaptive Monte Carlo algorithm for Wigner kernel evaluation. Neural Comput & Applic 32, 9953-9964 (2020). https://doi.org/10.1007/s00521-019-04519-9.
- Wigner E. (1932) On the quantum correction for thermodynamic equilibrium, Phys. Rev. 40: 749, https://doi.org/10.1103/PhysRev.40.749.