  We are interested in quantum systems composed of a finite number of particles
and described by Hamiltonians which are random Schrodinger operators
$H^{\omega}:=-\Delta + V^{\omega} $ on $L^2(X)$, where $X$ is a finite
dimensional Euclidean space and $\Delta$ is the Laplace-Beltrami operator on
$X$. We consider $X$ as the configuration space of the system and we assume
that $\{X_n\}_{1\leqslant n \leqslant N_0}$ is a family of linear subspaces of
$X$. The orthogonal complement of $X_n$ in $X$ is denoted $X^{n}$ and is
considered as the configuration space of a subsystem. We assume that
$V^{\omega}$ is a sum of potentials $v_n^{\omega}: X \longrightarrow \R,\quad
1\leqslant n \leqslant N_0,$ which are ergodic with respect the translation
group of $X_n$ and which are rapidly decaying in any direction of $X^{n}.$ The
aim of this paper is to show the existence of a thermodynamical limit. This
limit defines an object which is a type of a the integrated density of states
in the case of two body systems.
