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An Efficient Adaptive Monte Carlo Approach for Multidimensional Quantum Mechanics

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Recent Advances in Computational Optimization (WCO 2021)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 1044))

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Abstract

In this work we study an efficient adaptive approach for computing multidimensional problem in quantum mechanics. Richard Feynman’s problem for Wigner kernel (Feynman 1948; Wigner 1932) evaluation is well known multidimensional problem in quantum mechanics and nowadays there is renewing interest in finding solutions to this problem. We propose some improvements over the standard adaptive approach for the multidimensional integrals representing the Wigner kernel under consideration. The developed full Monte Carlo adaptive approach represents an important advantage in the context of quantum many-body simulations and can be important in the field of quantum chemistry.

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Acknowledgements

Venelin Todorov is supported by the Bulgarian National Science Fund under Project KP-06-M32/2 - 17.12.2019 “Advanced Stochastic and Deterministic Approaches for Large-Scale Problems of Computational Mathematics” and Project KP-06-N52/2 “Perspective Methods for Quality Prediction in the Next Generation Smart Informational Service Networks”. The work is also supported by the Bulgarian National Science Fund KP-06-N52/5 “Efficient methods for modeling, optimization and decision making” and by the Bulgarian National Science Fund under the Bilateral Project KP-06-Russia/17 “New Highly Efficient Stochastic Simulation Methods and Applications”.

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Authors and Affiliations

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

    Venelin Todorov

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

    Venelin Todorov & Ivan Dimov

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  1. Venelin Todorov
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  2. Ivan Dimov
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Correspondence to Venelin Todorov .

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Editors and Affiliations

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

    Stefka Fidanova

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Todorov, V., Dimov, I. (2022). An Efficient Adaptive Monte Carlo Approach for Multidimensional Quantum Mechanics. In: Fidanova, S. (eds) Recent Advances in Computational Optimization. WCO 2021. Studies in Computational Intelligence, vol 1044. Springer, Cham. https://doi.org/10.1007/978-3-031-06839-3_18

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