Contributions of subleading eigenvalues of 饾摏0 to the half-chain waiting-time distribution

Determine the contributions of the nonleading eigenvalues of the superoperator 饾摏0鈥攄efined by removing the jump superoperators associated with a monitored half-chain subsystem M from the full Lindblad Liouvillian with particle-number jump operators鈥攖o the half-chain waiting-time distribution, specifically establishing how the eigenvalue 位1 with the second-largest real part affects subleading corrections and possible crossover behavior at intermediate times.

Background

The paper analyzes waiting-time distributions (WTDs) of quantum jumps in continuously monitored many-body systems and shows that, for a half-chain subsystem, the long-time tail deviates from a Poissonian form and is governed by the leading eigenvalue 位0 of the superoperator 饾摏0. The operator 饾摏0 is constructed by subtracting jump terms in the monitored subsystem from the full Liouvillian.

While the leading behavior is controlled by 位0, the authors note that the influence of other eigenvalues of 饾摏0 on the WTD is not yet understood. Clarifying the role of the next-to-leading eigenvalue 位1 and possible intermediate-time crossovers would extend the spectral framework beyond the leading asymptotics.

References

While the long-time tail of the half-chain WTD is governed by the eigenvalue 位0 of the superoperator 饾摏0 with the largest real part, the role of the remaining eigenvalues is an open question. In particular, it is interesting to clarify how the eigenvalue 位1 with the second-largest real part contributes to the half-chain WTD, and whether it leads to characteristic subleading corrections or crossover behavior at intermediate times.

— Anomalous waiting-time distributions in postselection-free quantum many-body dynamics under continuous monitoring  (2604.00358 - Yamamoto et al., 1 Apr 2026) in Section 5 (Conclusions)