Vladimir Filinov

For deeper understanding of quantum non-local correlations a new path integral \textit{real--time} quantum dynamics approach has been developed and applied to the Monte Carlo simulation of the decoherence of pair entangled states in many--body systems in the framework of the ``replica trick''. Calculations have been carried out for the Heisenberg--Wigner path integral representation of the entangled state correlation function (ESCF) in the modified unified electron gas model as example. The Wiener--Khinchin transformation of ESCF has been applied to random paths in path integral allowing for the Monte Carlo simulation of ESCF. Presented results include the spin--resolved radial distribution functions, the ESCF and estimations of the decoherence time of the entangled electron pairs due to thermalization and interparticle interaction.

The Wigner formulation of quantum mechanics is used to derive a path-integral representation of the quantum density of states (DOS) of strongly correlated fermions in the canonical ensemble. A path-integral Monte Carlo approach for the simulation of DOS and other thermodynamic functions is suggested. The derived Wigner function in the phase space resembles the Maxwell-Boltzmann distribution but allows for quantum effects. We consider a three-dimensional quantum system of strongly correlated soft-sphere fermions at different densities and temperatures. The calculated properties include the DOS, momentum distribution functions, spin-resolved radial distribution functions, potentials of mean force, and related energy levels obtained from the Bohr-Sommerfeld condition. We observe sharp peaks on DOS and momentum distribution curves, which are explained by the appearance of fermionic bound states.

Path-integral Monte Carlo simulations in the Wigner approach to quantum mechanics has been applied to calculate momentum and spin-resolved radial distribution functions of the strongly correlated soft-sphere quantum fermions. The obtained spin-resolved radial distribution functions demonstrate arising triplet clusters of fermions, that is the consequence of the interference of exchange and interparticle interactions. The semiclassical analysis in the framework of the Bohr-Sommerfeld quantization condition, applied to the potential of the mean force corresponding to the same-spin radial distribution functions, allows to detect exchange-correlation bound states in triplet clusters and to estimate corresponding averaged energy levels. The obtained momentum distribution functions demonstrate the narrow sharp separated peaks corresponding to bound states and disturbing the Maxwellian distribution.

The Wigner formulation of quantum mechanics is used to derive a new path integral representation of quantum density of states (DOSs). A path integral Monte Carlo approach is developed for the numerical investigation of DOSs, internal energy and spin-resolved radial distribution functions for a 2D system of strongly correlated soft-sphere fermions. The peculiarities of the DOSs and internal energy distributions depending on the hardness of the soft-sphere potential and particle density are investigated and explained. In particular, at high enough densities the DOSs rapidly tends to a constant value, as for an ideal system of 2D fermions.

In this paper we continued our research of the uniform electron gas in a warm dense matter regime, focusing on the momentum distribution functions and pair correlation functions. We use the single–momentum path integral Monte Carlo method, based on the Wigner formulation of quantum statistics to calculate both momentum- and coordinate-depending distributions and average values of quantum operators for many-fermion Coulomb systems. We discovered that the single-particle momentum distribution function deviates from the ideal Fermi distribution and forms the so-called “quantum tails” at high momenta, if non-ideality is strong enough in both degenerate and non-degenerate cases. This effect is always followed by the appearance of the short-range order on pair correlation functions and can be explained by the tunneling through the effective potential wells surrounding the electrons. Furthermore, we calculated the average kinetic and potential energies in the wide range of states, expanding our previous results significantly.

A recently developed fermionic path integral Monte Carlo approach [Filinov et al., Phys. Rev. E 102, 033203 (2020) and Filinov et al., J. Phys. A 55, 035001 (2021)] has been applied for the estimation of the density–temperature range of exchange–correlation exciton existence in a strongly coupled degenerate uniform electron gas. The approach allows us to reduce the “fermionic sign problem” taking into account the interference effects of the Coulomb and exchange interaction of electrons in the basic Monte Carlo cell and its periodic images. Our results for radial distribution functions demonstrate the formation and decay of a short-range quantum ordering of electrons associated with exchange–correlation excitons in the literature. Such excitons have never been observed earlier in standard path integral Monte Carlo simulations.

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.