Accepted Thursday Nov 05, 2009
We introduce a dynamical matrix model where the matrix is interpreted as a Hamiltonian representing interaction of a bosonic system with a single fermion. We show how a system of second-quantized fermions influences the ground state of the whole system by producing a gap between the highest eigenvalue of the occupied single-fermion states and the lowest eigenvalue of the unoccupied single-fermion states. We describe the development of the gap in both, strong and weak coupling regime, while for the intermediate coupling strength we expect formation of homolumo "kinks".