東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Application of effective field theor...

Bhattacharyya, Anirban.

Linked to FindBook

Google Book

Amazon

博客來

Application of effective field theory to density functional theory for finite systems.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Application of effective field theory to density functional theory for finite systems./
Author:	Bhattacharyya, Anirban.
Description:	225 p.
Notes:	Adviser: R. J. Furnstahl.
Contained By:	Dissertation Abstracts International66-06B.
Subject:	Physics, Nuclear. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3180619
ISBN:	9780542209673

Application of effective field theory to density functional theory for finite systems.
Bhattacharyya, Anirban.

Application of effective field theory to density functional theory for finite systems. - 225 p.

Adviser: R. J. Furnstahl.

Thesis (Ph.D.)--The Ohio State University, 2005.

Density functional theory (DFT) is a tool of many-body physics whose popularity has grown over the years, primarily because it provides a useful balance between accuracy and computational cost, allowing large systems to be treated in a simple self-consistent manner. Effective field theory (EFT) is a framework which allows us to study the low-energy phenomena of a system in a systematic fashion. In this thesis, EFT methods are applied to DFT as part of a program to systematically go beyond mean-field approaches to medium and heavy nuclei. A system of fermions with short-range, natural interactions and an external confining potential (e.g., fermionic atoms in an optical trap) serves as a laboratory for studying DFT/EFT. An effective action formalism leads to a Kohn-Sham DFT by applying an inversion method order-by-order in the EFT expansion parameter. Results showing the convergence of Kohn-Sham calculations at zero temperature in the local density approximation (LDA) are compared to Thomas-Fermi calculations and to power-counting estimates. When conventional Kohn-Sham DFT for Coulomb systems is extended beyond the local density approximation, the kinetic energy density tau is sometimes included in energy functionals in addition to the fermion density. However, a local (semi-classical) expansion of tau is used to write the energy as a functional of the density alone, in contrast to the Skyrme approach. The difference is manifested in different single-particle equations, which in the Skyrme case include a spatially varying effective mass. The EFT framework for DFT is generalized to reconcile these approaches. An effective action approach is used to illustrate how the exact Green's function can be calculated in terms of the Kohn-Sham Green's function. An example based on Skyrme energy functionals shows that single-particle Kohn-Sham spectra can be improved by adding sources used to construct the energy functional. Finally, spin-orbit interactions are incorporated in the formalism leading to an energy functional having the same form as that of the Skyrme functional. Gradient expansions in terms of the local Fermi momentum are also worked out, which will be of use in the immediate future.

ISBN: 9780542209673Subjects--Topical Terms:

1019065
Physics, Nuclear.

Application of effective field theory to density functional theory for finite systems.
LDR:03094nam 2200265 a 45 001 971807
005 20110927
008 110927s2005 eng d
020 $a 9780542209673
035 $a (UnM)AAI3180619
035 $a AAI3180619
040 $a UnM $c UnM
100 1 $a Bhattacharyya, Anirban. $3 1295836
245 1 0 $a Application of effective field theory to density functional theory for finite systems.
300 $a 225 p.
500 $a Adviser: R. J. Furnstahl.
500 $a Source: Dissertation Abstracts International, Volume: 66-06, Section: B, page: 3200.
502 $a Thesis (Ph.D.)--The Ohio State University, 2005.
520 $a Density functional theory (DFT) is a tool of many-body physics whose popularity has grown over the years, primarily because it provides a useful balance between accuracy and computational cost, allowing large systems to be treated in a simple self-consistent manner. Effective field theory (EFT) is a framework which allows us to study the low-energy phenomena of a system in a systematic fashion. In this thesis, EFT methods are applied to DFT as part of a program to systematically go beyond mean-field approaches to medium and heavy nuclei. A system of fermions with short-range, natural interactions and an external confining potential (e.g., fermionic atoms in an optical trap) serves as a laboratory for studying DFT/EFT. An effective action formalism leads to a Kohn-Sham DFT by applying an inversion method order-by-order in the EFT expansion parameter. Results showing the convergence of Kohn-Sham calculations at zero temperature in the local density approximation (LDA) are compared to Thomas-Fermi calculations and to power-counting estimates. When conventional Kohn-Sham DFT for Coulomb systems is extended beyond the local density approximation, the kinetic energy density tau is sometimes included in energy functionals in addition to the fermion density. However, a local (semi-classical) expansion of tau is used to write the energy as a functional of the density alone, in contrast to the Skyrme approach. The difference is manifested in different single-particle equations, which in the Skyrme case include a spatially varying effective mass. The EFT framework for DFT is generalized to reconcile these approaches. An effective action approach is used to illustrate how the exact Green's function can be calculated in terms of the Kohn-Sham Green's function. An example based on Skyrme energy functionals shows that single-particle Kohn-Sham spectra can be improved by adding sources used to construct the energy functional. Finally, spin-orbit interactions are incorporated in the formalism leading to an energy functional having the same form as that of the Skyrme functional. Gradient expansions in terms of the local Fermi momentum are also worked out, which will be of use in the immediate future.
590 $a School code: 0168.
650 4 $a Physics, Nuclear. $3 1019065
690 $a 0610
710 2 0 $a The Ohio State University. $3 718944
773 0 $t Dissertation Abstracts International $g 66-06B.
790 $a 0168
790 1 0 $a Furnstahl, R. J., $e advisor
791 $a Ph.D.
792 $a 2005
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3180619