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

The master equation describing non-equilibrium one-dimensional problems like diffusion limited reactions or critical dynamics of classical spin 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 applications. At the same time physical intuition and probabilistic methods bring new insight into the understanding of the properties of quantum chains. A simple example is the asymmetric diffusion of several species of particles which leads naturally to Hecke algebras and q-deformed quantum groups. Many other examples are given. Several relevant technical aspects like critical exponents, correlation functions, and finite-size scaling are also discussed in detail. (C) 1994 Academic Press, Inc