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We investigate the D0-D4-brane system for different B-field backgroundsincluding the small instanton singularity in noncommutative SYM theory. Wediscuss the excitation spectrum of the unstable state as well as for the BPSD0-D4 bound state. We compute the tachyon potential which reproduces thecomplete mass defect. The relevant degrees of freedom are the massless (4,4)strings. Both results are in contrast with existing string field theorycalculations. The excitation spectrum of the small instanton is found to beequal to the excitation spectrum of the fluxon solution on R^2_theta x R whichwe trace back to T-duality. For the effective theory of the (0,0) stringexcitations we obtain a BFSS matrix model. The number of states in theinstanton background changes significantly when the B-field becomes self-dual.This leads us to the proposal of the existence of a phase transition or crossover at self-dual B-field.Comment: a4 11pt Latex2e 40 pages; v2: typos fixed, refined comments on  renormalisation, refs added, v3: ref added, version publishe

D0-D4 brane tachyon condensation to a BPS state and its excitation spectrum in noncommutative super Yang-Mills theory