"Did Van Dorn leave any troops in Arkansas when he crossed the Miss. river."
He left one man, Brig. Gen. John S. Roane.
While there were some scattered companies of men being organized at the time they were far from being anywhere like effective enough to be of any concern to Gen. Curtis and his Federal Army.
In one report in late May of 1862, a month after Van Dorn left, Roane stated that he had only 8 companies of infantry and 1 regiment of Cavalry available for the defence of Little Rock.
There is much speculation as to who these units were. But it is my belief that the Infantry were those men who eventually became the 26th Arkansas Infantry which were being organized in Pine Bluff in May. And the Cavalry was Parson's 12th Texas Cavalry, which Roane had stopped at Pine Bluff on their way to join Van Dorn.