drowse

Short definition from Wiktionary

Verb

1. 1
   To make (someone or something) heavy with drowsiness or sleepiness.
2. 2
   Followed by away: to pass (time) drowsily or in sleeping; also, to proceed (on a way) drowsily or sleepily.
3. 3
   To make (someone or something) dull or inactive, as if from sleepiness.
4. 4
   Often followed by away or off: to be drowsy or sleepy; to be half-asleep.
5. 5
   To be dull or inactive, as if from sleepiness.

Noun

1. 1
   An act, or a state, of being drowsy or sleepy.
2. 2
   A state of dullness or inactivity, as if from sleepiness.