Some Quantum Dynamical Semi-groups with Quantum Stochastic Dilation
Operator Algebras
2015-05-21 v1
Abstract
We consider the GNS Hilbert space of a uniformly hyper-finite - algebra and study a class of unbounded Lindbladian arises from commutators. Exploring the local structure of UHF algebra, we have shown that the associated Hudson-Parthasarathy type quantum stochastic differential equation admits a unitary solution. The vacuum expectation of homomorphic co-cycle, implemented by the Hudson-Parthasarathy flow, is conservative and gives the minimal semi-group associated with the formal Lindbladian. We also associate conservative minimal semi-groups to another class of Lindbladian by solving the corresponding Evan-Hudson equation.
Cite
@article{arxiv.1505.05296,
title = {Some Quantum Dynamical Semi-groups with Quantum Stochastic Dilation},
author = {Lingaraj Sahu and Preetinder Singh},
journal= {arXiv preprint arXiv:1505.05296},
year = {2015}
}