Concentration connotes a tightening of the will; reverie, a loose state of mind where the mind is allowed to wander a bit. Reverie is a form of concentration without that too-purposeful tightening up. My best ideas arise out of reverie, not concentration.
Writing, unfortunately, is highly dependent on states of mind. That is kind of a curse, because having to be "in the mood" can eliminate 90% of times when you have a spare moment or a free afternoon to write. Moods can be triggered, however. The best way to enter a state conducive to writing is to begin writing. The right mood will kick in--or not--after you've started.
Another trick is to notice when it happens and try to reproduce that feeling artificially on another day by remembering what it was like.
Experiment with muscular tension. Try to write while keeping your arm and shoulder muscles as tight as possible, then loosen them until you feel them almost drooping. Try to find that sweet spot where there is no unnecessary tension.
In music, a reverie is "an instrumental piece suggesting a dreamy or musing state." Think Andrew Hill, or Claude Debussy. Certain passages from Wordsworth evoke that feeling too.