Can cats have PTSD?

We recently adopted a cat a few months ago, and she is very sweet. Something that has happened a lot, however, is that at random moments, she will suddenly jerk her head to the left or right, almost as if she was expecting something. She also can be very calm one moment, then run off scared the next.

I know it might seem like a silly question, but we believe that our cat was once in an abusive home, so could she have some form of anxiety or PTSD? If so, what can we do to calm her down in anxious moments?

Thanks,

John