  We show that noisy nonunitary dynamics of bosons drives arbitrary initial
states into a novel fluctuating bunching state, where all bosons occupy one
time-dependent mode. We propose a concept of the noisy spectral gap, a
generalization of the spectral gap in noiseless systems, and demonstrate that
the exponentially fast absorption to the fluctuating bunching state takes place
asymptotically. The fluctuating bunching state is unique to noisy nonunitary
dynamics, with no counterpart in any unitary dynamics and nonunitary dynamics
described by a time-independent generator. We also argue that the times of
relaxation to the fluctuating bunching state obey a universal power law as
functions of the noise parameter in generic noisy nonunitary dynamics.
