One-dimensional solution of an extended time-dependent hartree-fock theory

1985 ◽  
Vol 163 (1-4) ◽  
pp. 14-20 ◽  
Author(s):  
M. Tohyama
Keyword(s):  
Time Dependent ◽  
Extended Time ◽  
Dimensional Solution ◽  
One Dimensional ◽  
Hartree Fock

scholarly journals Josephson oscillations in split one-dimensional Bose gases

2021 ◽  
Vol 10 (4) ◽  
Author(s):  
Yuri Daniel van Nieuwkerk ◽  
Jörg Schmiedmayer ◽  
Fabian Essler
Keyword(s):  
Three Dimensional ◽  
Time Dependent ◽  
Dimensional Theory ◽  
Bose Gases ◽  
Microscopic Description ◽  
One Dimensional ◽  
Hartree Fock ◽  
Equilibrium Dynamics ◽  
Self Consistent ◽  
Double Well Potential

We consider the non-equilibrium dynamics of a weakly interacting Bose gas tightly confined to a highly elongated double well potential. We use a self-consistent time-dependent Hartree--Fock approximation in combination with a projection of the full three-dimensional theory to several coupled one-dimensional channels. This allows us to model the time-dependent splitting and phase imprinting of a gas initially confined to a single quasi one-dimensional potential well and obtain a microscopic description of the ensuing damped Josephson oscillations.

EFFECT OF ELECTRON CORRELATION ON THE TWO-PARTICLE DYNAMICS OF A HELIUM ATOM IN A STRONG LASER PULSE

2002 ◽  
Vol 16 (03) ◽  
pp. 415-452 ◽  
Author(s):  
NILS ERIK DAHLEN
Keyword(s):  
Laser Pulse ◽  
Helium Atom ◽  
Electron Correlation ◽  
Density Functional ◽  
Femtosecond Laser Pulses ◽  
Time Dependent ◽  
Electron Dynamics ◽  
Dimensional Model ◽  
One Dimensional ◽  
Hartree Fock

This review discusses the complicated two-electron dynamics of a helium atom in an intense, short laser pulse. A helium gas in femtosecond laser pulses at long wave lengths (λ~700 nm) and high intensities (I~1015 W /cm2) produces surprisingly high numbers of He2+ ions. These laser fields cause large and fast electron oscillations, which makes a solution of the time-dependent Schrödinger equation numerically demanding. The system can be studied using a one-dimensional model atom, which has many of the same properties as the He atom. Using the one-dimensional model, the importance of including electron correlation in a simplified description of the two-electron dynamics is demonstrated. It is shown that electron correlation becomes much less important if the laser field has a short wave length, in which case the electron oscillations are smaller and slower. The problem of including electron correlation in the calculations is discussed in terms of approaches such as time-dependent Hartree–Fock, time-dependent density functional theory and time-dependent extended Hartree–Fock. Some of the commonly used semi-classical models for describing the double-ionization process are presented.

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