That's odd, because in the martial arts I do (aikido), I've always been amazed by how similar of a state it puts you into: trying to get into the zone, concentrate on what you're doing right now, and block any other distractions.
I'm doing silat. Many of our trainings are kinda "clocked", meaning you do the movements in a certain pace, so you don't have time to get distracted in the first place.