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Improved Stochastic Approaches for Evaluation of the Wigner Kernel

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Recent Advances in Computational Optimization (WCO 2020)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 986))

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Abstract

We compute the Wigner kernel by means of stochastic approaches. In this paper we study an optimized Adaptive Monte Carlo algorithm for evaluation of the Wigner kernel. This is an important problem in quantum mechanics represented by difficult multidimensional integrals. The goal of our work is to present an improved adaptive Monte Carlo algorithm and to compare the results with other stochastic approaches for computing the Wigner kernel in 3,6,9-dimensional case. It is important that 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 Monte Carlo algorithm under consideration has also been presented. It can be seen some advantages of the improved adaptive approach over the original one.

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Acknowledgements

Venelin Todorov is supported by the National Scientific Program “Information and Communication Technologies for a Single Digital Market in Science, Education and Security (ICT in SES)”, contract No DO1-205/23.11.2018, financed by the Ministry of Education and Science in Bulgaria and by the Bulgarian National Science Fund under Young Scientists Project KP-06-M32/2 - 17.12.2019 “Advanced Stochastic and Deterministic Approaches for Large-Scale Problems of Computational Mathematics”. The work is supported by the Bulgarian National Science Fund under Projects DN 12/5-2017 “Efficient Stochastic Methods and Algorithms for Large-Scale Problems” and KP-06-Russia/17 “New Highly Efficient Stochastic Simulation Methods and Applications”.

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Authors and Affiliations

  1. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Department of Information Modeling, Acad. Georgi Bonchev Str., Block 8, 1113, Sofia, Bulgaria

    Venelin Todorov & Stoyan Poryazov

  2. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Department of Parallel Algorithms, Acad. G. Bonchev Str., Block 25 A, 1113, Sofia, Bulgaria

    Venelin Todorov & Ivan Dimov

Authors
  1. Venelin Todorov
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  2. Ivan Dimov
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  3. Stoyan Poryazov
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Correspondence to Venelin Todorov .

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Editors and Affiliations

  1. Institute of Information and Communication Technology, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Stefka Fidanova

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Todorov, V., Dimov, I., Poryazov, S. (2022). Improved Stochastic Approaches for Evaluation of the Wigner Kernel. In: Fidanova, S. (eds) Recent Advances in Computational Optimization. WCO 2020. Studies in Computational Intelligence, vol 986. Springer, Cham. https://doi.org/10.1007/978-3-030-82397-9_23

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