  Non-universal dynamics is shown to occur in a one-dimensional non-equilibrium
system of hard-core particles. The stochastic processes included are pair
creation and annihilation (with rates e and e') and symmetric hopping rates
which alternate from one bond to the next (Pa, Pb). A dynamical scaling
relation between the relaxation time and the correlation length in the steady
state is derived in a simple way for the case e' > Pa >> Pb >> e. We find that
the dynamical exponent takes the non-universal value z = 2 ln(e'/e)/ln[(Pb
e')/(Pa e)]. For the special condition e + e'= Pa + Pb, where the stochastic
system is in principle soluble by reduction to a free fermion system, the model
is mapped to the Glauber dynamics of an Ising chain with alternating
ferromagnetic bonds of values J1 and J2, in contact with a quantum thermal
bath. The full time dependence of the space-dependent magnetization and of the
equal time spin-spin correlation function are studied by writing the master
equation for this system in the quantum Hamiltonian formalism. In particular we
obtain the dispersion relations and rigorously confirm the results obtained for
the correlation length and for the dynamical exponent.
