Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physics Letters A

Density response and correlation functions in the Wigner path integral representation. Monte Carlo simulations

Vladimir S. Filinov, Pavel R. Levashov, Alexander S. Larkin

Published Apr 15, 2025• 2 citations
Publisher
DOI
10.1016/j.physleta.2025.130542

Related papers

Wigner Distributions as Representations of the Density Matrix

Leon W. Cohen

Springer eBooks•Jan 1, 1987•2 citations

Phase-space path-integral representation of the quantum density of states: Monte Carlo simulation of strongly correlated soft-sphere fermions

Vladimir S. Filinov, Pavel R. Levashov, Alexander S. Larkin

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.

Physical review. E•Feb 27, 2024•3 citations

Density Matrix and the Wigner Distribution Function

IMPERIAL COLLEGE PRESS eBooks•Jan 1, 2006•0 citations

Decoherence of the pair entangled states at thermalization and interparticle interaction. Heisenberg--Wigner path integral Monte Carlo simulations

V. S. Filinov, Pavel R. Levashov, A. S. Larkin

For deeper understanding of quantum non-local correlations a new path integral 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, ESCFs and estimations of the decoherence time of the entangled electron pairs due to thermalization and interparticle interaction.

arXiv:2610.26033•Oct 19, 2026•0 citations

Density Matrix and the Wigner Distribution Function

WORLD SCIENTIFIC eBooks•Feb 19, 2017•0 citations

Bound States of the Exchange—Correlation Excitons in the Uniform Electron Gas by the Monte Carlo Simulations

Vladimir S. Filinov, Alexander S. Larkin, Pavel R. Levashov

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.

Universe•Jan 27, 2022•8 citations
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.
For deeper understanding of quantum non-local correlations a new path integral 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, ESCFs and estimations of the decoherence time of the entangled electron pairs due to thermalization and interparticle interaction.
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.