We present a simple microscopic model to show how fluctuating two--level systems in the Josephson junction tunnel barrier of thickness
L can modify the potential energy of the barrier and produce critical current noise spectra. We find low frequency
1/f noise that goes as
. Our values are in good agreement with recent experimental measurements of critical current noise in Al/AlO
/Al
... [Show full abstract] Josephson junctions. We also investigate the sensitivity of the noise on the nonuniformity of the tunnel barrier.