Who are the L.A.P.D officers in white hats?

All LAPD Officers now wear the dark blue (LAPD Blue) hats, regardless of rank, no major police department on the west coast uses white hats to denote rank.

I believe, what you are referring to is the white hat that used to worn by LAPD Traffic Division, and that was a long time ago.

Lapd Hat

In real police dept. the higher ranking officers, Sgt., Lt. Capt., etc. wear the white hats to signify their rank in the dept.