EIGENMODES OF DECAY AND FRAGMENTATION PROCESSES

Linear rate equations are used to describe the cascading decay of, e.g ., a jet into partons or an initial heavy nucleus into fragments. This representation is based upon a triangular matrix of transition rates. We expand the state vector of mass multiplicities, which describes th e process into the biorthonormal basis of eigenmodes provided by the t riangular matrix. We obtain analytic solutions of discrete models with explicit mathematical properties for the eigenmodes. A suitable conti nuous limit, valid for large systems, provides a solution interpolatin g between the solvable discrete cases. It gives a general relationship between the decay products and the elementary transition rates.