A New Optimized Adaptive Approach for Estimation of the Wigner Kernel

• Autorzy: Todorov Venelin , Fidanova Stefka , Dimov Ivan , Poryazov Stoyan

Identyfikatory

DOI

10.15439/2020F111

• Konferencja: Federated Conference on Computer Science and Information Systems (15 ; 06-09.09.2020 ; Sofia, Bulgaria)
• Języki publikacji: EN

Abstrakty

EN

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 3,6,9-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.

Słowa kluczowe

EN

Monte Carlo methods; quantum theory; stochastic processes

PL

Metody Monte Carlo; teoria kwantowa; procesy stochastyczne

• Wydawca: Polskie Towarzystwo Informatyczne
• Czasopismo: Annals of Computer Science and Information Systems
• Rocznik: 2020
• Tom: Vol. 21
• Strony: 341--344
• Opis fizyczny: Bibliogr. 5 poz., wz., wykr., tab.

Twórcy

autor

Todorov Venelin

• Bulgarian Academy of Sciences, Institute of Mathematics and Informatics, ul. G. Bonchev 8, 1113 Sofia, Bulgaria
• Bulgarian Academy of Sciences, Institute of Information and Communication Technologies, ul. G. Bonchev 25A, 1113 Sofia, Bulgaria

autor

Fidanova Stefka

• Bulgarian Academy of Sciences, Institute of Information and Communication Technologies, ul. G. Bonchev 25A, 1113 Sofia, Bulgaria

autor

Dimov Ivan

• Bulgarian Academy of Sciences, Institute of Information and Communication Technologies, ul. G. Bonchev 25A, 1113 Sofia, Bulgaria

autor

Poryazov Stoyan

• Bulgarian Academy of Sciences, Institute of Mathematics and Informatics, ul. G. Bonchev 8, 1113 Sofia, Bulgaria

Bibliografia

• 1. 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.
• 2. Feynman R.P. (1948) Space-time approach to nonrelativistic quantum mechanics, Rev. Mod. Phys. 20, https://doi.org/10.1103/RevModPhys.20.367.
• 3. 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.
• 4. 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.
• 5. Wigner E. (1932) On the quantum correction for thermodynamic equilibrium, Phys. Rev. 40: 749, https://doi.org/10.1103/PhysRev.40.749.

Uwagi

1. Track 1: Artificial Intelligence

2. Technical Session: 13th International Workshop on Computational Optimization

3. Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).