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SUMMARY:The quantum first detection problem: from the energy spectrum to t
he detection probabilities
DTSTART;VALUE=DATE-TIME:20170906T100000Z
DTEND;VALUE=DATE-TIME:20170906T101500Z
DTSTAMP;VALUE=DATE-TIME:20230207T091200Z
UID:indico-contribution-77@zakopane.if.uj.edu.pl
DESCRIPTION:Speakers: Felix Thiel (Bar-Ilan University)\, David A. Kessler
(Bar-Ilan University)\, Eli Barkai (Bar-Ilan University)\n\nWe consider t
he question of when a quantum system initially prepared in state A first `
`arrives'' in state B\, i.e. the first arrival problem in quantum physics.
\nTo determine the arrival\, the observer attempts to detect the system st
roboscopically with fixed period via a projective measurement.\nThe time o
f the first successful detection attempt is the first detection time.\nThe
corresponding probability of the event is the first detection probability
.\nFor systems with a continuous energy spectrum\, this quantity can be ex
pressed in terms of the spectral measure of the evolution operator (which
is related to the density of energy states).\nThis allows us to present an
exact formula for the total probability of detection and to derive the lo
ng-time asymptotic behavior of the first detection probabilities.\nIt is s
hown that the latter decays like a power law with superimposed oscillation
s.\nThe exponent of the power law is determined by the spectral (or fracto
n) dimension of the spectral measures.\nThe total probability of detection
is always less than unity.\n\nhttps://zakopane.if.uj.edu.pl/event/4/contr
ibutions/77/
LOCATION:Aula
RELATED-TO:indico-event-4@zakopane.if.uj.edu.pl
URL:https://zakopane.if.uj.edu.pl/event/4/contributions/77/
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