ACAD SINICA,INST HIGH ENERGY PHYS,BEIJING 100039,PEOPLES R CHINA
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 the process into the biorthonormal basis of eigenmodes provided by the triangular matrix. We obtain analytic solutions of discrete models with explicit mathematical properties for the eigenmodes. A suitable continuous limit, valid for large systems, provides a solution interpolating between the solvable discrete cases. It gives a general relationship between the decay products and the elementary transition rates.