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{\Large \bf NGF vs. First Principle Simulations for Quantum Coulomb Systems}\\
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{\large \underline{M.~Bonitz}$^{1}$, D.~Semkat$^{1}$, A.~Filinov$^{1}$, V.~Golubnychyi$^{1}$,
 V.~Filinov$^{2}$}

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$^{1}$FB Physik, Rostock University, D-18051 Rostock, Germany\\
%$^2$Theoretical Division, Los Alamos National Laboratory\\
$^2$High Energy Density Center of the RAS, Moscow\\
%$^4$FB Physik, Philipps-Universit\"at Marburg, Germany\\
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\noindent
Nonequilibrium Green's Functions (NGF) methods have proven to be very successfull for the description of
correlated degenerate Coulomb systems in plasmas and solids. Most importantly, the internal consistency
of the method allows for straightforward incorporation of external fields even on femtosecond time scales,
thereby fully preserving correct conservation of total energy.
In particular, direct solutions of the equations of motion for the two-time correlation functions
have been demonstrated for optically excited semiconductors [1] and for plasma oscillations of correlated
electrons for weak and strong excitation [2]. Recently, these methods have been successfully extended
to ultracold ions in traps, e.g. Semkat et al. [3].

However, strong correlation effects in Coulomb systems which require to go beyond the second Born
approximation are hardly feasible within the present NFG schemes. On the other hand,
these problems are well accessible for computer simulations, such as
Quantum Monte Carlo or classical and quantum molecular dynamics. An overview on recent simulation
results is given which includes atom and molecule formation [4] and Wigner crystallization [5]. Finally,
the limitations of these methods are discussed and compared to the NGF approach. Interestingly,
strengths and limitations are complementary raising the idea to combine NGF with
first-principle simulations.



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\noindent [1] N.H.~Kwong et al., phys. stat. sol. (b) {\bf 206}, 197 (1998)

\noindent [2] N.H.~Kwong, and M.~Bonitz, Phys. Rev. Lett. {\bf 84}, 1768 (2000)

%\noindent [1] D. Semkat, D. Kremp, and M. Bonitz,
              Phys. Rev. E {\bf 59}, 1557 (1999)

\noindent [3] Poster at this workshop.

%\noindent [1] M.~Bonitz, Physik-Journal, No. 7/8 (2002) 69-75

\noindent [4] V.~Filinov, V.E.~Fortov, M.~Bonitz, and P.~Levashov,
JETP Letters {\bf 74}, 384 (2001)

\noindent [5] A.~Filinov, M.~Bonitz, and Yu.E.~Lozovik, Phys. Rev. Lett. {\bf 86}, 3851 (2001) and
Phys. Rev. Focus April 2002

%\noindent [4] V.~Filinov, et al., Phys. Rev. B {\bf 65}, 165124 (2002)

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