ACF plot in Non Stationary Time Sereis

#1
Hello Folks
I know that in non-stationary time series, the Auto Correlation Function plot dies down extremely slowly while if the series is stationary, ACF cuts off or dies down fairly quickly. I want to know the statistical reason behind this. Why does ACF die down slowly if the series is not stationary. Can you relate this to unit roots. I mean by using formal math?