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The gap of the Liouvillian spectrum gives the asymptotic decay rate of aquantum dissipative system, and therefore its inverse has been identified asthe slowest relaxation time. In contrary to this common belief, we show thatthe relaxation time due to diffusive transports in a boundary dissipatedmany-body quantum system is determined not by the gap or low-lying eigenvaluesof the Liouvillian but by superexponentially large expansion coefficients forLiouvillian eigenvectors with non-small eigenvalues at an initial state. Thisfinding resolves an apparent discrepancy reported in the literature between theinverse of the Liouvillian gap and the relaxation time in dissipative many-bodyquantum systems.

Resolving Discrepancy between Liouvillian Gap and Relaxation Time in Boundary-Dissipated Quantum Many-Body Systems