Repeated interaction processes in the continuous-time limit, applied to quadratic fermionic systems
Mathematical Physics
2020-02-19 v1 math.MP
Abstract
We study a class of Lindblad equation on finite-dimensional fermionic systems. The model is obtained as the continuous-time limit of a repeated interaction process between fermionic systems with quadratic Hamiltonians, a setup already used by Platini and Karevski for the one-dimensional XY model. We prove a necessary and sufficient condition for the convergence to a unique stationary state, which is similar to the Kalman criterion in control theory. Several examples are treated, including a spin chain with interactions at both ends.
Cite
@article{arxiv.1903.08223,
title = {Repeated interaction processes in the continuous-time limit, applied to quadratic fermionic systems},
author = {Simon Andreys},
journal= {arXiv preprint arXiv:1903.08223},
year = {2020}
}
Comments
34 pages, 3 figures