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We show that noisy nonunitary dynamics of bosons drives arbitrary initialstates into a novel fluctuating bunching state, where all bosons occupy onetime-dependent mode. We propose a concept of the noisy spectral gap, ageneralization of the spectral gap in noiseless systems, and demonstrate thatthe exponentially fast absorption to the fluctuating bunching state takes placeasymptotically. The fluctuating bunching state is unique to noisy nonunitarydynamics, with no counterpart in any unitary dynamics and nonunitary dynamicsdescribed by a time-independent generator. We also argue that the times ofrelaxation to the fluctuating bunching state obey a universal power law asfunctions of the noise parameter in generic noisy nonunitary dynamics.

Absorption to Fluctuating Bunching States in Non-Unitary Boson Dynamics