Has anyone seen research that demonstrates dedicating different computers to specific tasks (separated by physical distance) increases productivity?
Not research, but I've seen people comment anecdotally that using the iPad/tablet for fun stuff and the laptop for work trains them that time wasting shouldn't occur on the laptop.
I've experienced the same thing using spaces/desktops on the Mac. If a time waster app isn't in my current space/desktop, I don't use it when on an important task. The browser is a fine line and requires discipline though so not as good as a separate device. Works for games though - those are only on the iPad.
I couldn't imagine why having two or more devices for different work types would help. I've noticed that if I'm in the mood to slack off I'll find a way of doing it regardless.
If you're having problems concentrating on a task for very long before your mind starts wandering then you should perhaps try something like the Pomodoro technique. You basically just tell yourself you'll do something for 25 mins then take a 5 minute break. More info here http://www.pomodorotechnique.com/
For what it's worth I've not used the Pomodoro technique, I've used a subset of GTD so I've constantly got a list of things to be working on. I've noticed that if I check that list I'm often able to continue to get things done, whilst I've got the energy (today for example I don't have much energy, which is why I'm checking out this site).