Extended operator algebra for abelian sandpile models

Deepak Dhar

Physica A: Statistical Mechanics and its Applications, 1996, vol. 224, issue 1, 162-168

Abstract: We generalize the definition of the operators corresponding to particle addition in the abelian sandpile models to include a phase factor eiϵn, where n is the number of topplings in the avalanche, and ϵ is a real parameter. The new operators so defined are still abelian, and their derivatives with respect to ϵ satisfy an equation similar to the Heisenberg equation for the time-derivative of operators in standard quantum mechanics. The role of the Hamiltonian is played by the toppling function, an operator linear in the height variables of the sandpile, which does not commute with the particle addition operators. We show that moments of the distribution of the number of topplings in avalanches in the steady state are expressed in a simple way in terms of these operators.

Date: 1996
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0378437195003207
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:224:y:1996:i:1:p:162-168

DOI: 10.1016/0378-4371(95)00320-7

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().