The main aim of the present paper is to provide a new construction of quantum Markov chain (QMC) on arbitrary order Cayley tree. In that construction, a QMC is defined as a weak limit of finite volume states with boundary conditions, i.e. QMC depends on the boundary conditions. Note that this construction reminds statistical mechanics models with competing interactions on trees. If one considers one dimensional tree, then the provided construction reduces to well-known one, which was studied by the first author. Our construction will allow to investigate phase transition problem in a quantum setting.
|Journal||Journal of Physics: Conference Series|
|Publication status||Published - Mar 24 2016|
|Event||International Conference on Algebra, Analysis and Quantum Probability - Tashkent, Uzbekistan|
Duration: Sept 10 2015 → Sept 12 2015
ASJC Scopus subject areas
- Physics and Astronomy(all)