Reaction-Diffusion Processes, Critical Dynamics and Quantum Chains
摘要
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 -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.
引用
@article{arxiv.hep-th/9302112,
title = {Reaction-Diffusion Processes, Critical Dynamics and Quantum Chains},
author = {Francisco C. Alcaraz and Michel Droz and Malte Henkel and Vladimir Rittenberg},
journal= {arXiv preprint arXiv:hep-th/9302112},
year = {2016}
}
备注
Latex 52 pages (2 figures appended at the end), UGVA-DPT 1992/12-799