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With {\it RXTE} data, we analyzed the cross-correlation function between thesoft and hard X-rays of the transient atoll source 4U 1608-52. We foundanti-correlations in three outbursts occurred in 1998, 2002 and 2010, andsignificant time lags of several hundreds of seconds in the latter twooutbursts. Our results show no correlation between the soft and hard X-rays inthe island state, and a dominated positive correlation in the lower bananastate. Anti-correlations are presented at the upper banana state for theoutburst of 2010 and at the lower left banana states for the other twooutbursts. So far for atoll sources the cross-correlation has been studiedstatistically only for 4U 1735-44, where anti-correlations showed up in theupper banana state. Here our investigation upon 4U 1608-52 provides a similarresult in its 2010 outburst. In addition, we notice that the luminosities inthe upper banana of 1998 and 2002 outbursts are about 1.5 times that of 2010outburst whose luminosity in the upper banana is close to that of 4U 1735-44.The results suggest that the states in color-color diagram of a source could becorrelated with the luminosity of the source. A further spectral analysis showsthat, during the 2010 outburst, although an anti-correlation presents at thehighest fluxes, the contemporary spectrum is not the softest one along theoutburst evolution. This suggests that the observed anti-correlation may berelevant to the transition between the hard and soft states, which isconsistent with the previous results on 4U 1735-44 and several black hole X-raybinaries that anti-correlations are observed during the transition states.

The properties of cross-correlation and spectra of the low-mass X-ray binary 4U 1608-52