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 Matem. Mod., 2010, Volume 22, Number 11, Pages 79–96 (Mi mm3042)

Feinman path integral computer simulation of helium atom electron shell

S. V. Shevkunov

Saint Petersburg State Polytechnic University, Saint Petersburg

Abstract: Ab inition calculations of electron-electron and electron-nucleus space correlation functions in the ground state of helium atom with explicit account for the exchange and spin variables are carried out using Feinman Path Integral Monte Carlo method. Mechanical properties of the electron shell are obtained in terms of the volume-pressure dependence. The dependencies of energy on as well as its components are calculated in the conditions of a strong shock compression. In thermally excited states, the phenomenon of spin “pairing” accompanying the cooling and compression of the system is studied. The spin squared operator equilibrium numbers dependencies are calculated. It is demonstrated that, even in the low temperature regime, Path Integral Monte Carlo method in the field of Coulomb singularity preserves its effectiveness, and fluctuation uncertainties of the basic energy estimator are reducing when cooling the system. The convergence of discretized presentation of Feinman integral at low temperatures is provided due to natural reduction of the lengths of links of the path drawn into the field of the nucleus.

Keywords: path integrals, quantum statistics, computer simulation, Monte Carlo method, electrons, exchange symmetry, spin.

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Citation: S. V. Shevkunov, “Feinman path integral computer simulation of helium atom electron shell”, Matem. Mod., 22:11 (2010), 79–96

Citation in format AMSBIB
\Bibitem{She10} \by S.~V.~Shevkunov \paper Feinman path integral computer simulation of helium atom electron shell \jour Matem. Mod. \yr 2010 \vol 22 \issue 11 \pages 79--96 \mathnet{http://mi.mathnet.ru/mm3042} 

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This publication is cited in the following articles:
1. Shevkunov S.V., “Exchange and Spin States in Quantum Dots Under Strong Spatial Correlations. Computer Simulation by the Feynman Path Integral Method”, J. Exp. Theor. Phys., 117:4 (2013), 699–717
2. S. V. Shevkunov, “Spin states of electrons in quantum dots upon heating. Simulation by the Feynman path integral method. Structure”, High Temperature, 54:6 (2016), 782–788
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