This is the first piece on my "Insomnia" playlist: the second movement of Sergei Prokofiev's Violin Concerto No. 2 in G minor, II. Andante assai. I don't think there's much need for explanation, but here's a link to program notes from the San Francisco Symphony website.
For those curious, the recording above is of violinist Zino Francescatti with the New York Philharmonic conducted by Dimitri Mitropoulos on October 27, 1952.