  We derive and solve a Fokker-Planck equation for the stationary distribution
of the free energy, in a model of unzipping of double-stranded DNA under
external force. The autocorrelation function of the random DNA sequence can be
a general form, including long range correlations. In the case of
Orstein-Uhlenbeck noise, characterized by a finite correlation length, our
result reduces to the exact result of Allahverdyan et al, with the average
number of unzipped base pairs going as <X>~1/f^2 in the white noise limit,
where f is the deviation from the critical force. In the case of long range
correlated noise, where the integrated autocorrelation is divergent, we find
that <X> is finite at f=0, with its value decreasing as the correlations become
longer range. This shows that long range correlations actually stabilize the
DNA sequence against unzipping. Our result is also in agreement with the
findings of Allahverdyan et al, obtained using numerical generation of the long
range correlated noise.

Statistical Mechanics;Soft Condensed Matter;Biological Physics