Reaction-Diffusion Processes, Critical Dynamics and Quantum Chains

Details Reaction-Diffusion Processes, Critical Dynamics and Quantum Chains Reaction-Diffusion Processes, Critical Dynamics and Quantum Chains

1993-02-23

arxiv.org/abs/hep-th/9302112v1

Annals Phys. 230 (1994) 250-302

Physics

High Energy Physics

High Energy Physics - Theory

Latex 52 pages (2 figures appended at the end), UGVA-DPT 1992/12-799

Scientific paper

10.1006/aphy.1994.1026

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 Schr\"odinger 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.

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