Reaction-diffusion processes and their connection with integrable quantum spin chains

Details Reaction-diffusion processes and their connection with integrable quantum spin chains Reaction-diffusion processes and their connection with integrable quantum spin chains

2003-03-24

arxiv.org/abs/cond-mat/0303512v2

Physics

Condensed Matter

Statistical Mechanics

Latex, 38 pages, 6 figures, uses amsfonts,amssymb,amsbsy,graphicx. To be published in ``Classical and Quantum Nonlinear Integr

Scientific paper

This is a pedagogical account on reaction-diffusion systems and their relationship with integrable quantum spin chains. Reaction-diffusion systems are paradigmatic examples of non-equilibrium systems. Their long-time behaviour is strongly influenced through fluctuation effects in low dimensions which renders the habitual mean-field cinetic equations inapplicable. Starting from the master equation rewritten as a Schr\"odinger equation with imaginary time, the associated quantum hamiltonian of certain one-dimensional reaction-diffusion models is closely related to integrable magnetic chains. The relationship with the Hecke algebra and its quotients allows to identify integrable reaction-diffusion models and, through the Baxterization procedure, relate them to the solutions of Yang-Baxter equations which can be solved via the Bethe ansatz. Methods such as spectral and partial integrability, free fermions, similarity transformations or diffusion algebras are reviewed, with several concrete examples treated explicitly. An outlook on how the recently-introduced concept of local scale invariance might become useful in the description of non-equilibrium ageing phenomena is presented, with particular emphasis on the kinetic Ising model with Glauber dynamics.

Affiliated with

Also associated with

No associations

Rating

Reaction-diffusion processes and their connection with integrable quantum spin chains does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Reaction-diffusion processes and their connection with integrable quantum spin chains, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Reaction-diffusion processes and their connection with integrable quantum spin chains will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-448903