  The statistical properties of heart beat intervals of 130 long-term surface
electrocardiogram recordings during atrial fibrillation (AF) are investigated.
We find that the distribution of interbeat intervals exhibits a characteristic
exponential tail, which is absent during sinus rhythm, as tested in a
corresponding control study with 72 healthy persons. The rate of the
exponential decay lies in the range 3-12 Hz and shows diurnal variations. It
equals, up to statistical uncertainties, the level of the previously uncovered
white noise part in the power spectrum, which is also characteristic for AF.
The overall statistical features can be described by decomposing the intervals
into two statistically independent times, where the first one is associated
with a correlated process with 1/f noise characteristics, while the second one
belongs to an uncorrelated process and is responsible for the exponential tail.
It is suggested to use the rate of the exponential decay as a further parameter
for a better classification of AF and for the medical diagnosis. The relevance
of the findings with respect to a general understanding of AF is pointed out.
