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Dobaczewski .pdf



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Ab initio derivation of model EDFs
Jacek Dobaczewski
University of York, University of Jyväskylä, University of Warsaw
Bridging nuclear ab-initio and EDF theories
Orsay, France, 2-6 October 2017
Jacek Dobaczewski

1/24

Ab initio project in collaboration with:
• Gianluca Salvioni, Jyväskyla
• Karim Bennaceur, Lyon

• Carlo Barbieri, Surrey

• Andrea Idini, Surrey

• Gillis Carlsson, Lund

• Alessandro Pastore, York
Jacek Dobaczewski

2/24

Outline
1. Ab initio DFT
2. Ab initio derivations of nuclear DFT
3. Conclusions

Jacek Dobaczewski

3/24

Density Functional Theory:
A variational method that uses
a two-step variational
procedure.

Levy and Lieb construction,
see Chapter 3.4 in R.G. Parr and W. Yang
Density-Functional Theory of Atoms and Molecules
(New York, Oxford University Press, 1989)

J. D., J. Phys.: Conf. Ser. 312, 092002 (2011)

What is DFT?

Jacek Dobaczewski

4/24

A two-step variation
I

23

22

19

34

21

42

22

21

34

20

19

II

21

25

43

24

21

32

32

18

31

29

18

III

38

27

30

24

23

27

22

42

23

32

22

IV

21

23

31

32

27

35

20

21

26

37

20

V

32

22

36

25

22

23

21

25

34

33

21

VI

32

20

21

32

35

36

27

31

22

21

20

VII

31

33

42

32

25

31

42

29

31

23

23

VIII

24

29

24

32

42

23

34

45

32

27

23

Jacek Dobaczewski

5/24

Density Functional Theory:
A variational method that uses
a two-step variational
procedure.
Divide all states into groups that have the
same densities, an then:
1. Find the lowest energy in each group
(very, very, difficult)
2. Find the lowest energy among all groups
(relatively easy)

J. D., J. Phys.: Conf. Ser. 312, 092002 (2011)

What is DFT?

Jacek Dobaczewski

6/24

Density Functional Theory:
A variational method that uses
observables as variational
parameters.

J. D., J. Phys.: Conf. Ser. 312, 092002 (2011)

What is DFT?

Jacek Dobaczewski

7/24

J. D., J. Phys.: Conf. Ser. 312, 092002 (2011)

Which DFT?

Jacek Dobaczewski

8/24

Density Functional Theory:
Exact: A variational method
that uses a two-step variational
procedure with observables
used for the variational
parameters.
Practical: Build a model of
density functional.

J. D., J. Phys.: Conf. Ser. 312, 092002 (2011)

What is DFT?

Jacek Dobaczewski

9/24


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