The phrase "am brown study" implies deep thought and concentration, but there are several antonyms that convey a lack of focus or mental lethargy. One such antonym is "mindlessness," which refers to a lack of awareness or attention. Another antonym is "scatterbrained," which conveys a disorganized or unfocused mental state. "Distraction" is yet another antonym, suggesting that one's attention is constantly pulled away from the task at hand. Finally, "carelessness" suggests a lack of concern or attention to details, in contrast to the careful focus implied by the phrase "am brown study.