# 32nd M. Smoluchowski Symposium on Statistical Physics

18-21 September 2019
Kraków
Europe/Warsaw timezone

## Non-Hermitean and Zeno limit of the quantum first detection problem

19 Sep 2019, 15:00
30m
Kraków

Talk

### Speaker

Dr. Felix Thiel (Bar-Ilan University)

### 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.

### Primary author

Dr. Felix Thiel (Bar-Ilan University)

### Co-authors

Prof. Eli Barkai (Bar-Ilan University) Prof. David A. Kessler (Bar-Ilan University)

### Presentation Materials

There are no materials yet.
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