REACTION-DIFFUSION PROCESSES, CRITICAL-DYNAMICS, AND QUANTUM CHAINS

The master equation describing non-equilibrium one-dimensional problem s like diffusion limited reactions or critical dynamics of classical s pin systems can be written as a Schrodinger equation in which the wave function is the probability distribution and the Hamiltonian is that of a quantum chain with nearest neighbor interactions. Since many one- dimensional quantum chains are integrable, this opens a new field of a pplications. At the same time physical intuition and probabilistic met hods bring new insight into the understanding of the properties of qua ntum chains. A simple example is the asymmetric diffusion of several s pecies of particles which leads naturally to Hecke algebras and q-defo rmed quantum groups. Many other examples are given. Several relevant t echnical aspects like critical exponents, correlation functions, and f inite-size scaling are also discussed in detail. (C) 1994 Academic Pre ss, Inc