  We study the large N dynamics of two massless Yang-Mills coupled matrix
quantum mechanics, by minimization of a loop truncated Jevicki-Sakita effective
collective field Hamiltonian. The loop space constraints are handled by the use
of master variables. The method is successfully applied directly in the
massless limit for a range of values of the Yang-Mills coupling constant, and
the scaling behaviour of different physical quantities derived from their
dimensions are obtained with a high level of precision. We consider both planar
properties of the theory, such as the large N ground state energy and
multi-matrix correlator expectation values, and also the spectrum of the
theory. For the spectrum, we establish that the U(N) traced fundamental
constituents remain massless and decoupled from other states, and that bound
states develop well defined mass gaps, with the mass of the two degenerate
lowest lying bound states being determined with a particularly high degree of
accuracy. In order to confirm, numerically, the physical interpretation of the
spectrum properties of the U(N) traced constituents, we add masses to the
system and show that, indeed, the U(N) traced fundamental constituents retain
their "bare masses". For this system, we draw comparisons with planar results
available in the literature.
