  We study a system of two tunnel-coupled quantum dots, with the first dot
containing interacting electrons (described by the Universal Hamiltonian) not
subject to spin-orbit coupling, whereas the second contains non-interacting
electrons subject to spin-orbit coupling. We focus on describing the behavior
of the system near the Stoner transition. Close to the critical point quantum
fluctuations become important and the system enters a quantum critical regime.
The large-$N$ approximation allows us to calculate physical quantitites
reliably even in this strongly fluctuating regime. In particular, we find a
scaling function to describe the crossover of the quasiparticle decay rate
between the renormalized Fermi liquid regime and the quantum critical regime.
