An exact Jordan signature in cumulative-count first-passage statistics
quant-ph, math-ph, math.MP
Submitted: 2026-09-17
Updated: 2026-09-18
Comments: Substantially revised and narrowed. Corrects the earlier exceptional-point interpretation, clarifies counted self-transitions and terminal-summed visibility, and adds an exact three-state Markov-renewal example with a nonzero N8^{-N} Jordan term and square-root eigenvalue ramification. The mechanism is classical; the Lindblad model is an embedding
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Terminology
Sources
- Full counting statistics and first-passage times in quantum Markovian processes: Ensemble relations, metastability, and fluctuation theorems
- Counting quantum jumps: a summary and comparison of fixed-time and fluctuating-time statistics in electron transport
- Semi-Markov Processes in Open Quantum Systems. III. Large Deviations of First Passage Time Statistics
- Keldysh's theorem revisited
- Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps
- Topological transitions in quantum jump dynamics: Hidden exceptional points
- Computing Large Deviations of First-Passage-Time Statistics in Open Quantum Systems: Two Methods
- Bounds on Fluctuations of First Passage Times for Counting Observables in Classical and Quantum Markov Processes
- Quantum jump trajectories, hybrid systems, non-Hermitian evolutions, quantum/classical walks
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