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\title{
Tunneling of identical interacting fermions: \\ A quantum molecular dynamics study}
\author{Yu.~E.~Lozovik$^{1}$
\thanks{E-mail: lozovik@isan.troitsk.ru. Fax: (+7095)334-0886.},
A.~V.~Filinov$^{1,2}$, A.~S.~Arkhipov$^{1}$}
\address{$^1$ Institute of Spectroscopy RAS, Moscow region, Troitsk, Russia,142190 \\
$^2$ Fachbereich Physik, Universit{\"a}t Rostock\\
Universit{\"a}tsplatz 3, D-18051 Rostock, Germany}

\maketitle
We demonstrate a new method of simulating nonstationary quantum
processes. We consider the problem of nonstationary tunneling
of two interacting identical particles represented by wave
packets. The method of quantum molecular dynamics (QMD) based on
the Wigner representation of quantum mechanics is applied. 
In the context
of the method, ensembles of classical trajectories are used to solve
the quantum Wigner-Liouville equation. These classical trajectories obey
Hamilton-like equations, where the force consists of the usual classical
term and a quantum correction depending on the Wigner function and its
derivatives. 
The quantum term is calculated using a local distribution
of trajectories in phase space, therefore the trajectories
are not independent as in classical molecular dynamics.
The developed QMD method takes into account the influence of exchange and
interaction between particles simultaneously. 
The role of direct and exchange interactions on the
tunneling process is analyzed and  characteristic 
tunneling times for interacting particles are estimated.

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