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SUMMARY:On maximal chaos exponent for theories with a global symmetry (Par
t II)
DTSTART;VALUE=DATE-TIME:20190814T060000Z
DTEND;VALUE=DATE-TIME:20190814T070000Z
DTSTAMP;VALUE=DATE-TIME:20191212T105859Z
UID:indico-event-7290@cern.ch
DESCRIPTION:In this note we study chaos in generic quantum systems with a
global symmetry generalizing seminal work [arXiv : 1503.01409] by Maldacen
a\, Shenker and Stanford. We conjecture a bound on chaos exponent in a the
rmodynamical ensemble at temperature T and chemical potential μ for the g
lobal symmetry under consideration. For local operators which could create
excitations upto some fixed charge\, the bound on chaos (Lyapunov) expone
nt is independent of chemical potential λL ≤ / 2πTℏ\;. On the other
hand when the operators could create excitations of arbitrary high charge\
, we find that exponent must satisfy λ_L ≤ / 2 π T (1- abs \\ μ μc
ℏ where μc is the maximum value of chemical potential for which the the
rmodynamic ensemble makes sense. As specific examples of quantum mechanica
l systems we consider conformal field theories. In a generic conformal fie
ld theory with internal U(1) symmetry living on a cylinder the former boun
d is applicable\, whereas in more interesting examples of holographic two
dimensional conformal field theories dual to Einstein gravity\, we argue t
hat later bound is saturated in presence of a non-zero chemical potential
for translation or rotation.\n\nhttps://indico.tifr.res.in/indico/conferen
ceDisplay.py?confId=7290
LOCATION: A 304
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=7290
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