D branes in 2d String Theory and Classical limits

In the matrix model formulation of two dimensional noncritical string theory, a D0 brane is identified with a single eigenvalue excitation. In terms of open string quantities (i.e fermionic eigenvalues) the classical limit of a macroscopically large number of D0 branes has a smooth classical limit : they are described by a filled region of phase space whose size is O(1) and disconnected from the Fermi sea. We show that while this has a proper description in terms of a {\em single} bosonic field at the quantum level, the classical limit is rather nontrivial. The quantum dispersions of bosonic quantities {\em survive in the classical limit} and appear as additional fields in a semiclassical description. This reinforces the fact that while the open string field theory description of these D-branes (i.e. in terms of fermions) has a smooth classical limit, a closed string field theory description (in terms of a single boson) does not