Gaussian phase-space representation of Fermion dynamics; Beyond the time-dependent-Hartree-Fock approximation
arXiv:0902.3227 · doi:10.1103/PhysRevB.79.165103
Abstract
A Gaussian operator representation for the many body density matrix of fermionic systems, developed by Corney and Drummond [Phys. Rev. Lett, v93, 260401 (2004)], is used to derive approximate decoupling schemes for their dynamics. In this approach the reduced single electron density matrix elements serve as stochastic variables which satisfy an exact Fokker-Planck equation. The number of variables scales as ~N^2 rather than ~exp(N) with the basis set size, and the time dependent Hartree Fock approximation (TDHF) is recovered in the "classical" limit. An approximate closed set of equations of motion for the one and two-particle reduced density matrices, provides a direct generalization of the TDHF.
12 pages. Minor revision, reference added
References in corpus (12)
- A real-space, rela-time method for the dielectric function
- Density Operators for Fermions
- A Generalized Fluctuation-Dissipation Theorem for Nonlinear Response Functions
- Gaussian quantum Monte Carlo methods for fermions
- Gauge P-representations for quantum-dynamical problems: Removal of boundary terms
- Gaussian phase-space representations for fermions
- Gaussian operator bases for correlated fermions
- Gaussian-Basis Monte Carlo Method for Numerical Study on Ground States of Itinerant and Strongly Correlated Electron Systems
- Symmetry projection schemes for Gaussian Monte Carlo methods
- Generalized coherent state representation of Bose-Einstein condensates
- Quasiparticle Density-Matrix Representation of Nonlinear TDDFT Response Functions
- Systematic errors in Gaussian Quantum Monte Carlo and a systematic study of the symmetry projection method
Cited by in corpus (7)
- Semiclassical approach to Dynamics of Interacting Fermions
- Linear entropy in quantum phase space
- Stochastic simulations of fermionic dynamics with phase-space representations
- First-principles quantum dynamics for fermions: Application to molecular dissociation
- On the Dynamics of the Fermi-Bose Model
- Simulations of quantum dynamics with fermionic phase-space representations using numerical matrix factorizations as stochastic gauges
- Correlated quantum dynamics of graphene