BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Wannier functions for periodic Schrdinger operator
s and harmonic maps into the unitary group - Panat
i\, G (Universit degli Studi di Roma La Sapienza)
DTSTART;TZID=Europe/London:20150327T113000
DTEND;TZID=Europe/London:20150327T123000
UID:TALK58629AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/58629
DESCRIPTION:Co-author: Adriano Pisante ("La Sapienza" Universi
ty of Rome) \n\nThe localization of electrons in c
rystalline solids is often expressed in terms of t
he Wannier functions\, which provide an orthonorma
l basis of L2(Rd) canonically associated to a give
n periodic Schrdinger operator. \n\nA very popular
tool in theoretical and computational solid-state
physics are the maximally localized Wannier funct
ions\, which are defined as the minimizers (in a s
uitable space of Wannier functions) of a localizat
ion functional introduced by Marzari and Vanderbil
t in 1997. While early confirmed by numerical evid
ence\, the exponential localization of such minimi
zers has remained an open question until recently.
\n\nIn the talk\, the concept of Wannier basis wi
ll be reviewed in detail\, with emphasis on its ge
ometric counterpart (Bloch frame). Then a recent r
esult proving the existence and the exponential lo
calization of the minimizers\, under suitable assu
mptions\, will be presented (joint work with A. Pi
sante). The proof exploits methods and techniques
from the regularity theory of harmonic maps into t
he unitary group and the so-called "decomposition
into unitons" of such maps.\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
END:VEVENT
END:VCALENDAR