Nonlinear Schrodinger dynamics of matrix D-branes

We formulate an effective Schrodinger wave equation describing the quantum dynamics of a system of D0-branes by applying the Wilson renormalization gr oup equation to the world sheet partition function of a deformed sigma -mod el describing the system, which includes the quantum recoil due to the exch ange of string states between the individual D-particles. We arrive at an e ffective Fokker-Planck equation for the probability density with diffusion coefficient determined by the total kinetic energy of the recoiling system. We use Galilean invariance of the system to show that there are three poss ible solutions of the associated nonlinear Schrodinger equation depending o n the strength of the open string interactions among the D-particles. When the open string energies are small compared to the total kinetic energy of the system, the solutions are governed by freely-propagating solitary waves . When the string coupling constant reaches a dynamically determined critic al value, the system is described by minimal uncertainty wavepackets which describe the smearing of the D-particle coordinates due to the distortion o f the surrounding space-time from the string interactions. For strong strin g interactions, bound state solutions exist with effective mass determined by an energy-dependent shift of the static BPS mass of the D0-branes.