SPECTRA OF QUANTUM CHAINS WITHOUT THE YANG-BAXTER EQUATION

We study one-dimensional reaction-diffusion models described by master equations and their associated two-state quantum hamiltonians. By cho osing appropriate rates, the equations of motion decouple into certain subsets. We solve the first subset which has a close relation to the problem of lattice electrons in an electric field. In this way we obta in L(L - 1) + 1 energy levels of a quantum chain with L sites. The cor responding hamiltonian depends on seven parameters and does not look i ntegrable using conventional methods. As an application, we compute th e dynamical critical exponent of a new type of kinetic Ising model.