Abstract
The modified path integral representation of Wigner functions and the new Monte Carlo approach has been suggested to account for the impact of the interparticle interaction on the Pauli exclusion principle of fermions. This approach also allows to calculate the momentum distribution functions and to reduce the “sign problem” that is inaccessible to the standard path integral Monte Carlo methods. The obtained pair electron–electron distribution functions for the “uniform electron gas” demonstrate the short-range quantum ordering of electrons associated with exchange-correlation excitons. The exchange-correlation exciton is caused by the interaction of electrons with positively charged exchange holes and the excluded volume effect. The developed approach allows one to study the density–temperature range of the exciton arising, existence, and decay. Using the potential of the mean force and semiclassical Bohr–Sommerfeld quantization condition, we have demonstrated the existence of bound states disturbing the Maxwellian distribution and estimated their average energy levels. The exchange-correlation excitons have not been observed earlier in the standard path integral Monte Carlo simulations.
Highlights
Using the potential of the mean force and semiclassical Bohr–Sommerfeld quantization condition, we have demonstrated the existence of bound states disturbing the Maxwellian distribution and estimated their average energy levels
We present the results of the path integral Monte Carlo simulations in the Wigner approach (WPIMC) of the unpolarized UEG
With that in mind let us start from a twocomponent Coulomb system of quantum electrons and classical uncorrelated positive charges uniformly distributed in space, simulating the positive background
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. An alternative approach to quantum mechanics based on Wigner functions in the phase space [5,6] allows to overcome these disadvantages It allows to calculate quantum momentum distribution functions and transport properties of matter [3]. The obtained charge estimation of the exchange hole shows that its average positive charge is equal to the elementary charge, making the exchange-correlation exciton neutral This short-range screening validates a simple Fermi-liquid model of metals, in which nearly-free electrons are assumed. The electron momentum distribution functions (the Wigner functions) demonstrate the disturbance of the Maxwellian distribution by narrow sharp peaks due to the arising of the exciton bound states These physical effects were not observed earlier in the standard PIMC simulations. We demonstrate the stochastic nature of the energy levels disturbing the Maxwell distribution
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