2021/09/07 by Gilles G. de Castro, de Castro, Gilles G.
Mathematics · Physics and Astronomy · #46L30 #46L40 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA) #Primary: 46L55. Secondary: 37A55 #Quantum many-body systems
paper · pdf · doi:10.48550/arxiv.2109.03050
openalex publication_date 2021/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a self-similar K set defined from an iterated function system Γ=(γ1,…,γn) and a set of function H=\hi:K→ℝ\i=1d satisfying suitable conditions, we define a generalized gauge action on Kawjiwara-Watatani algebras OΓ and their Toeplitz extensions TΓ. We then characterize the KMS states for this action. For each β∈(0,∞), there is a Ruelle operator LH,β and the existence of KMS states at inverse temperature β is related to this operator. The critical inverse temperature βc is such that LH,βc has spectral radius 1. If ββc, including β=∞, the extreme points of the set of KMS states on TΓ are parametrized by the elements of K and on OΓ by the set of branched points.