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We note that this smallest root scales inversely with the threshold energyE B and is approximatelyλ NB 1 ≈2.404 2/(4EB)∝1/E B (see Ap- pendix B for details)

Long-time quasi-stationary surviving states At long times, the infinitely frequent measurement limit quantum first-passage density decays exponentially as∼e −λ NB 1 t whereλ NB 1 i

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Quantum-classical crossover in noisy monitored oscillators

quant-ph · 2026-08-08 · conditional · novelty 7.0

For a harmonic oscillator driven by classical noise, the first-passage-time distribution to an energy threshold under projective measurements is exactly a sum of exponentials with Laguerre-root rates, converging to the classical result only at high thresholds.

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  • Quantum-classical crossover in noisy monitored oscillators quant-ph · 2026-08-08 · conditional · none · ref 1

    For a harmonic oscillator driven by classical noise, the first-passage-time distribution to an energy threshold under projective measurements is exactly a sum of exponentials with Laguerre-root rates, converging to the classical result only at high thresholds.