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CATEGORIES:Theoretical Physics Seminars
SUMMARY:Wave Functions and Their Densities in Metric Space
- Prof Irene d'Amico\, U of York
DTSTART:20120223T134500Z
DTEND:20120223T150000Z
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URL:/talk/index/707
DESCRIPTION:Hilbert space combines the properties of two diffe
rent types of mathematical spaces: vector space an
d metric space. While the vector-space aspects are
widely used\, the metric-space aspects are much l
ess exploited. Here[1] we show that a suitable met
ric stratifies Fock space into concentric spheres
on which maximum and minimum distances between sta
tes can be defined and geometrically interpreted.
Unlike the usual Hilbert-space analysis\, our resu
lts apply also to the reduced space of only ground
states and to that of particle densities\, which
are metric\, but not Hilbert\, spaces. The Hohenbe
rg-Kohn mapping between densities and ground state
s\, which is highly complex and nonlocal in coordi
nate description\, is found\, for three different
model systems\, to be simple in metric space\, whe
re it becomes a monotonic and nearly linear mappin
g of vicinities onto vicinities.\n\n[1]Phys. Rev.
Lett. 106\, 050401 (2011)
LOCATION:Theory Library
CONTACT:Dr Dimitri M Gangardt
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