Repeated interaction processes in the continuous-time limit, applied to quadratic fermionic systems
arXiv:1903.08223 · doi:10.1007/s00023-019-00852-w
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.
34 pages, 3 figures
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