Full current statistics for a disordered open exclusion process. (2nd March 2016)

• Record Type: Journal Article
• Authors: Ayyer, Arvind
• Is Part Of: Journal of physics. Volume 49:Number 15(2016)
• Publication Date: 2016-03-02
• Subjects: nonequilibrium process -- current fluctuations -- large deviation function -- modified Doob transform; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8113/49/15/155003
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We consider the nonabelian sandpile model defined on directed trees by Ayyer et al (2015 Commun. Math. Phys. 335 1065 ) and restrict it to the special case of a one-dimensional lattice of n sites which has open boundaries and disordered hopping rates. We focus on the joint distribution of the integrated currents across each bond simultaneously, and calculate its cumulant generating function exactly. Surprisingly, the process conditioned on seeing specified currents across each bond turns out to be a renormalised version of the same process. We also remark on a duality property of the large deviation function. Lastly, all eigenvalues and both Perron eigenvectors of the tilted generator are determined.