Speaker
Description
The classical first-passage theory for random walks is generalized to quantum systems by using repeated attempts with a fixed frequency $1/\tau$ to find the system in the detection state $| \psi_\text{d}\rangle$. The first successful of these attempts defines the time $T = N \tau$ of first detected arrival. Here, the Zeno limit $\tau\to0$ of diverging detection frequency is investigated. The repeated detection setup is compared with a non-Hermitean Schrödinger equation. Using an electrostatic analogy we can determine all absorbtion modes in the Zeno limit and find the pdf as well as all moments of $T$ for systems with a discrete energy spectrum. The pdf has a scaling form in $\tau$. Applying known results from the repeated detection setup to the non-Hermitean equation shows that the mean dissipation time in the latter system is quantized.
