Absorption to Fluctuating Bunching States in Non-Unitary Boson Dynamics

We show that noisy non-unitary 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 exponentially fast absorption to the fluctuating bunching state takes place asymptotically. The fluctuating bunching state is unique to noisy non-unitary dynamics with no counterpart in any unitary dynamics and non-unitary 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 non-unitary dynamics.