NONUNIVERSAL DYNAMICS OF STAGGERED NONEQUILIBRIUM PARTICLE-SYSTEMS AND ISING CHAINS

Non-universal dynamics is shown to occur in a one-dimensional non-equi librium system of hard-core particles. The stochastic processes includ ed are pair creation and annihilation (with rates epsilon and epsilon' ) and symmetric hopping rates which alternate from one bond to the nex t (p(A), p(B)). A dynamical scaling relation between the relaxation ti me and the correlation length in the steady state is derived in a simp le way for the case epsilon' > p(A) >> p(B) >> epsilon. We find that t he dynamical exponent takes the non-universal value z = 2 ln(epsilon'/ epsilon)/ln(p(B) epsilon'/p(A) epsilon). For the special condition eps ilon + epsilon' = p(A) + p(B), where the stochastic system is in princ iple soluble by reduction to a free fermion system, the model is mappe d to the Glauber dynamics of an Ising chain with alternating ferromagn etic bonds of values J(1) and J(2), in contact with a quantum thermal bath. The full time dependence of the space-dependent magnetization an d of the equal time spin-spin correlation function are studied by writ ing the master equation for this system in the quantum Hamiltonian for malism. In particular, we obtain the dispersion relations and rigorous ly confirm the results obtained for the correlation length and for the dynamical exponent.