Sleep deprivation is linked to an increase in dopamine. I know this because I researched why I was able to concentrate better on nights with poor sleep compared to nights with great sleep.

Oddly enough, for people with ADHD, a poor sleeping schedule might actually help (in the short term) with concentration issues!

This!

I found in university, strangely through sheer accident, (during the first two years of my PhD program in physics) that I performed best on my final exams and written qualifiers with three hours of sleep.

I would sleep 3 hours after late-night study, drink a lot of coffee, and then be able to hyper-focus like a felon on a three-hour-long exam.

How was the recovery?

Not ideal, but in some cases manageable for several days.

Eg, I remember doing 3 qualifiers on Mon, Wed, and Fri in one week, so a small nap and then back to studying for the next one.

Not a fun week, that.

This phenomenon is usually followed by a deep slump in productivity after that dopamine rush wears off.

Oh absolutely, a day of poor sleep takes two days to recover from in my personal experience ;(