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SUMMARY:Non-Hermitean and Zeno limit of the quantum first detection proble
m
DTSTART;VALUE=DATE-TIME:20190919T130000Z
DTEND;VALUE=DATE-TIME:20190919T133000Z
DTSTAMP;VALUE=DATE-TIME:20230207T213600Z
UID:indico-contribution-323@zakopane.if.uj.edu.pl
DESCRIPTION:Speakers: Eli Barkai (Bar-Ilan University)\, David A. Kessler
(Bar-Ilan University)\, Felix Thiel (Bar-Ilan University)\n\nThe classical
first-passage theory for random walks is generalized to quantum systems b
y using repeated attempts with a fixed frequency $1/\\tau$ to find the sys
tem in the detection state $| \\psi_\\text{d}\\rangle$. The first successf
ul of these attempts defines the time $T = N \\tau$ of first *detected* ar
rival. Here\, the Zeno limit $\\tau\\to0$ of diverging detection frequency
is investigated. The repeated detection setup is compared with a non-Herm
itean Schrödinger equation. Using an electrostatic analogy we can determi
ne 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 detectio
n setup to the non-Hermitean equation shows that the mean dissipation time
in the latter system is quantized.\n\nhttps://zakopane.if.uj.edu.pl/event
/9/contributions/323/
LOCATION:Kraków
RELATED-TO:indico-event-9@zakopane.if.uj.edu.pl
URL:https://zakopane.if.uj.edu.pl/event/9/contributions/323/
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