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SUMMARY:Quantum first detection time
DTSTART;VALUE=DATE-TIME:20170904T130000Z
DTEND;VALUE=DATE-TIME:20170904T133000Z
DTSTAMP;VALUE=DATE-TIME:20220809T220905Z
UID:indico-contribution-148@zakopane.if.uj.edu.pl
DESCRIPTION:Speakers: Eli Barkai (Bar-Ilan University\, Israel)\nWe invest
igate the quantum first detection problem for a quantum walk \nusing proje
ctive measurement postulates. \nA simple relation between the measurement
free state function |psi> and |phi>_n is obtained\, \nthe latter\nis the
first detection amplitude at the n-th attempt. This relation is the quantu
m renewal equation\, its classical counter part is widely used to find sta
tistics of first passage time for random walks and Brownian motion. We inv
estigate statistics of first detection for open and closed systems (first
arrival or passage is not well defined in quantum theory). For closed sys
tems\, like a ring\, with a\ntranslation invariant Hamiltonian\, we find Z
eno physics\, optimum sampling times\, critical sampling effect related to
revivals\, dark states\, and quantisation of the mean detection time. For
a quantum walk on the line\, with particle starting on |x_i> and detected
on the origing |0>\, with a tight-binding Hamiltonian with hops to neares
t neighbours\, we find the detection probability decays like (time)^(-3) w
ith super imposed quantum oscillation\, thus the quantum exponent is doubl
e its classical counter part. The Polya problem is discussed\, and it is f
ound that in one dimension the total detection probability\, does not depe
nd on the initial distance of the particle from detector\, though survival
of the particle is not unity. There is an optimal sampling time which max
imises the\ntotal detection probability. \n\n$ $\n\nJoint work with Harel
Fridman\, David Kessler\, and Felix Thiel.\n\nhttps://zakopane.if.uj.edu.p
l/event/4/contributions/148/
LOCATION:
URL:https://zakopane.if.uj.edu.pl/event/4/contributions/148/
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