Atome im Computer - German Research School for Simulation

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Atome im Computer
Erik Koch
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Computational Materials Science
German Research School for Simulation Sciences
Riesenmagnetwiderstand
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Materialwissenschaften
Steinzeit
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Dreiperiodensystem
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Bronzezeit
Eisenzeit
Anfänge der Atomistik
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Johannes Kepler, 1611:
Neujahrsgabe oder
Vom sechseckigen Schnee
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Anfänge der Atomistik
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Johannes Kepler, 1611:
Neujahrsgabe oder
Vom sechseckigen Schnee
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X-Strahlen
Wilhelm Conrad Röntgen, 1895
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Die Hand von Frau Röntgen,
aufgenommen am 22. Dezember 1895.
Kristallstruktur
Max von Laue, Walter Friedrich und Paul Knipping,1912
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Übungsaufgabe
Gegeben:
Atome der Ordnungszahl Zα an den Positionen Rα.
Lösen Sie
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Ne
2 �
�
H=−
2m
j=1
∇2j −
1
4π�0
Ni
Ne �
�
j=1
2
Zα e
1
+
|r − Rα | 4π�0
α=1 j
Ne
�
j<k
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a
Ni
�
e
Zα Zβ e 2
1
+
|rj − rk | 4π�0
|Rα − Rβ |
2
The underlying laws necessary for the mathematical theory
of a large part of physics and the whole of chemistry are
thus completely known, and the difficulty is only that exact
applications of these laws lead to equations which are too
complicated to be soluble. It therefore becomes desirable that
approximate practical methods of applying quantum mechanics
should be developed, which can lead to an explanation of the
main features of complex atomic systems without too much
computation.
P.M.A. Dirac, Proceedings of the Royal Society A123, 714 (1929)
Theory of (almost) Everything
α<β
Reduktionismus
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sehr einfache Regeln
führen zu
simplem Verhalten
Reduktionismus
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einfache Regeln
führen zu
komplexem Verhalten
Formen des Kohlenstoffs
Diamant
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Formen des Kohlenstoffs
Graphit
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Buckminsterfullerenes: 1985
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Nano-Röhren: 1991
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Graphen: 2004
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Periodensystem
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Li
Be
B
C
Na
Mg
Al
Si
K
Ca
Sc
Ti
V
Cr
Mn
Fe
Co
Ni
Cu
Zn
Ga
Rb
Sr
Y
Zr
Nb
Mo
Tc
Ru
Rh
Pd
Ag
Cd
Cs
Ba
Lu
Hf
Ta
W
Re
Os
Ir
Pt
Au
Fr
Ra
Lr
Rf
Db
Sg
Bh
Hs
Mt
La
Ce
Pr
Nd
Pm
Sm
Eu
Gd
Ac
Th
Pa
U
Np
Pu
Am
Cm
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He
N
O
F
Ne
P
S
Cl
Ar
Ge
As
Se
Br
Kr
In
Sn
Sb
Te
I
Xe
Hg
Tl
Pb
Bi
Po
At
Rn
Tb
Dy
Ho
Er
Tm
Yb
Bk
Cf
Es
Fm
Md
No
Baukasten Periodensystem
MgB2 Supraleiter: 2000
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LaMnO3 colossal magnetoresistance
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FeAs Supraleiter: 2008
La2-xSrxCuO4 HiTc: 1987
Baukasten Periodensystem
Telefonnummer-Verbindungen
Ca14Cu24O41: 14-24-41
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organische Kristalle
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Die Rolle der Theorie
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Man siehtnnur,
s
was man
weiß
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Man sieht nur, was man weiss
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metallisch
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isolierend
CNT (n,m)
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n-m = 3l : metallisch
Einteilchenbild
t2g
gu
Aufbauprinzip
realistische Rechungen:
Dichtefunktional-Theorie (DFT)
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gg
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E in eV
g
t1g
t1u
0
hu
g
t2u u
-5
hg
ag
t1u
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gg + hg
Spin-Ladungs-Trennung
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Elektronenzerfall im korrelierten Festkörper
Theorie made in Aachen
Dynamical Mean-Field Theory (DMFT)
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Dynamical Mean-Field Theory
ersetze Kristallgitter
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Gloc (ω) =
�
n
s
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�
�−1
dk ω − µ − ε(k) − Σ(ω)
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−1
Gb−1 (ω) = Σ(ω) + Gloc
(ω)
durch Elementarzelle, die in ein
dynamisches Medium eingebettet ist
Gb−1 (ω)
≈ ω + µ − �0 −
HAnd = Hloc +
�
lσ
†
εlσ alσ
alσ
+
�
�
li,σ
l
Vli
|Vl |2
(ω − εl )
�
†
ciσ
alσ
−1
Σ(ω) = Gb−1 (ω) − Gimp
(ω)
Ein-Platz Problem
�
+ H.c.
Rechenzentrum, ca. 1890
OPINION BIG DATA
ESSAY
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NATURE|Vol 455|4 September 2008
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The Harvard computers1
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Observatories hired computers —
a term used for human processors
since the early 1700s
A photograph taken at the
Harvard Observatory in Cambridge, Massachusetts, circa
1890, features eight women in
what looks like a Victorianstyle sitting room. They wear long skirts, have
upswept hair and are surrounded by flowered
wallpaper and mahogany tables. At first glance
they seem to be sampler stitching or reading.
In fact these ‘human computers’ are analysing
photographs of the heavens, cataloguing stars.
When cameras were first attached to telescopes, with the ability to capture the image
of thousands of stars on a single photographic
plate, people were needed to trawl through
these new data. Observatories hired ‘computers’ — a term used for human processors
since the early 1700s — to do the painstakingly
repetitive work of measuring the brightness,
position and colours of these stars.
From the 1880s until the 1940s, the Harvard
College Observatory amassed half a million
photographic glass plates, weighing around
300 tonnes and holding images of tens of
millions of stars. A team of women trawled
through these photos with nothing more than
magnifying glasses — often for little pay and
with no scientific training.
Williamina Fleming stands in the centre of the Harvard computers as Edward Pickering looks on.
HARVARD COLL. OBSERV.
The first mass data crunchers were people, not machines. Sue Nelson looks at the
discoveries and legacy of the remarkable women of Harvard’s Observatory.
Heimcomputer, ca. 1951
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[…] all went smoothly until I had to face up to the problem of factoring highorder secular equations. I knew how to do this by hand, but the task was
time-consuming, and it was necessary to check and recheck the factoring to
make sure no errors were made. It then occurred to me that my mother
could help me with some of this work. I had read about the Hartrees how the
younger Hartree (Douglas R.) had been aided by his father (William), who was a
retired railroad engineer and enjoyed doing sums on a desk calculator. I
showed my mother how to set up the OPW secular equations and how to
factor them, and she agreed to do some of this in her spare time […]
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Frank Herman Elephants and mahouts —
early days in semiconductor physics
Physics Today, June 1984, p.56
Wachstum der Rechenleistung
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Wachstum der Rechenleistung
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desktop
Top 500 Supercomputer (Juni 2010)
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Jülicher Supercomputer: Jugene & Juropa
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massiv parallele Algorithmen
16384
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16 sites
18 sites
20 sites
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8192
speed up
4096
2048
1024
sites memory
512
16
1 GB
256
18
18 GB
20
254 GB
128
128
256
t
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512
1024 2048 4096 8192 16384
# CPU
realistische Theorie korrelierter Materialien
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