Nonequilibrium Green's functions approach to inhomogeneous systems:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2013
|
| Series: | Lecture Notes in Physics
867 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XII, 130 S. Ill., graph. Darst. |
| ISBN: | 9783642350818 |
Staff View
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Record in the Search Index
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IMAGE 1
CONTENTS
PART I INTRODUCTION 1 QUANTUM MANY-PARTICLE SYSTEMS OUT O F EQUILIBRIUM
3
1.1 OVERVIEW ON COMPUTATIONAL APPROACHES 5
1.2 MANY-BODY INTERACTIONS IN INHOMOGENEOUS QUANTUM SYSTEMS . . 7 1.3
CORRELATIONS 9
PART II THEORY
2 NONEQUILIBRIUM GREEN'S FUNCTIONS 15
2.1 INTRODUCTION 16
2.1.1 KELDYSH CONTOUR 17
2.1.2 ONE-PARTICLE NONEQUILIBRIUM GREEN'S FUNCTION 19
2.2 EQUATIONS OF MOTION 22
2.2.1 KELDYSH-KADANOFF-BAYM EQUATIONS 24
2.2.2 EQUILIBRIUM LIMIT. DYSON EQUATION 26
2.3 MANY-BODY APPROXIMATIONS 28
2.3.1 REQUIREMENTS FOR A CONSERVING SCHEME 29
2.3.2 PERTURBATION EXPANSIONS 29
2.4 QUANTUM KINETIC EQUATIONS FOR SINGLE-TIME QUANTITIES 33
2.4.1 THE RECONSTRUCTION PROBLEM FOR THE ONE-PARTICLE GREEN'S FUNCTION
34
2.4.2 THE GENERALIZED KADANOFF-BAYM ANSATZ 37
PART III COMPUTATIONAL METHODS
3 REPRESENTATIONS O F THE NONEQUILIBRIUM GREEN'S FUNCTION 41
3.1 NUMERICAL RESOURCES 41
3.1.1 HOMOGENEOUS SYSTEMS. A BRIEF OUTLINE 41
3.1.2 INHOMOGENEOUS SYSTEMS. COMPUTER MEMORY AS LIMITING FACTOR 44
3.2 GRID VERSUS BASIS REPRESENTATIONS FOR INHOMOGENEOUS SYSTEMS . . 44
I X
HTTP://D-NB.INFO/1027027245
IMAGE 2
X
C O N I E N T S
3.3 AN EFFICIENT SOLUTION: THE FINITE ELEMENT-DISCRETE VARIABLE
REPRESENTATION 47
3.3.1 GENERAL IDEA AND BACKGROUND 47
3.3.2 CONSTRUCTION OF THE FE-DVR BASIS 48
3.3.3 MATRIX ELEMENTS OF RELEVANT ENERGIES 51
3.3.4 FIRST- AND SECOND-ORDER SELF-ENERGIES 53
4 COMPUTATION O F EQUILIBRIUM STATES AND TIME-PROPAGATION 55
4.1 PREPARING THE INITIAL STATE: GROUND STATE OR EQUILIBRIUM 55
4.1.1 TIME OR FREQUENCY SPACE? 56
4.1.2 SOLUTION OF THE DYSON EQUATION IN R-SPACE 58
4.2 NONEQUILIBRIUM 6 0
4.2.1 TWO-TIME PROPAGATION METHOD 6 0
4.2.2 PARALLELIZATION STRATEGIES 63
4.2.3 SINGLE-TIME PROPAGATION USING THE GKBA 68
PART IV APPLICATIONS FOR INHOMOGENEOUS SYSTEMS
5 LATTICE SYSTEMS 75
5.1 OVERVIEW 76
5.2 A BASIC EXAMPLE 77
5.2.1 DYNAMICS FOLLOWING A NON-PERTURBATIVE EXCITATION . . . . 78 5.2.2
ABSORPTION SPECTRUM IN SECOND BORN APPROXIMATION . . . 80
6 NON-LATTICE SYSTEMS 83
6.1 SMALL ATOMS AND MOLECULES. GROUND STATE PROPERTIES AND RESPONSE TO
EXTERNAL FIELDS 83
6.1.1 MODEL-LIKE TREATMENT 84
6.1.2 3D ATOMS AND MOLECULES 94
6.2 FEW-ELECTRON QUANTUM DOTS AND WELLS 9 6
6.2.1 CORRELATION EFFECTS IN THE OPTICAL ABSORPTION SPECTRA . . . 98
6.2.2 ELECTRONIC DOUBLE EXCITATIONS FROM THE KADANOFF-BAYM EQUATIONS 100
7 CONCLUSION AND OUTLOOK 105
7.1 SUMMARY 105
7.2 PROSPECTS FOR FUTURE APPLICATIONS 106
APPENDIX A SECOND QUANTIZATION 109
A . L SYMMETRY O F MANY-BODY STATES 109
A.2 OCCUPATION NUMBER REPRESENTATION 110
A.3 PARTICLE CREATION AND ANNIHILATION IN FOCK SPACE I L L
A.4 GENERAL FORM OF OPERATORS 112
APPENDIX B PERTURBATION EXPANSION. SUPPLEMENTS 115
B . L DERIVATIVE OF A CONTOUR-ORDERED PRODUCT 115
B.2 EQUATIONS FOR 27 ^ AND S G ^ / S V ^ ^ IN TERMS OF * * * * 117
REFERENCES 119
INDEX 1 29 |
| any_adam_object | 1 |
| author | Balzer, Karsten 1980- Bonitz, Michael 1960- |
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| dewey-ones | 530 - Physics |
| dewey-raw | 530.14 |
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| isbn | 9783642350818 |
| language | English |
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| spelling | Balzer, Karsten 1980- Verfasser (DE-588)1018400915 aut Nonequilibrium Green's functions approach to inhomogeneous systems Karsten Balzer ; Michael Bonitz Berlin [u.a.] Springer 2013 XII, 130 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture Notes in Physics 867 Green-Funktion (DE-588)4158123-4 gnd rswk-swf Inhomogenes Medium (DE-588)4228459-4 gnd rswk-swf Nichtgleichgewicht (DE-588)4171730-2 gnd rswk-swf Quantenmechanisches System (DE-588)4300046-0 gnd rswk-swf Quantenmechanisches System (DE-588)4300046-0 s Inhomogenes Medium (DE-588)4228459-4 s Green-Funktion (DE-588)4158123-4 s Nichtgleichgewicht (DE-588)4171730-2 s DE-604 Bonitz, Michael 1960- Verfasser (DE-588)120375176 aut Erscheint auch als Online-Ausgabe 978-3-642-35082-5 Lecture Notes in Physics 867 (DE-604)BV000003166 867 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4164605&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025495619&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Balzer, Karsten 1980- Bonitz, Michael 1960- Nonequilibrium Green's functions approach to inhomogeneous systems Lecture Notes in Physics Green-Funktion (DE-588)4158123-4 gnd Inhomogenes Medium (DE-588)4228459-4 gnd Nichtgleichgewicht (DE-588)4171730-2 gnd Quantenmechanisches System (DE-588)4300046-0 gnd |
| subject_GND | (DE-588)4158123-4 (DE-588)4228459-4 (DE-588)4171730-2 (DE-588)4300046-0 |
| title | Nonequilibrium Green's functions approach to inhomogeneous systems |
| title_auth | Nonequilibrium Green's functions approach to inhomogeneous systems |
| title_exact_search | Nonequilibrium Green's functions approach to inhomogeneous systems |
| title_full | Nonequilibrium Green's functions approach to inhomogeneous systems Karsten Balzer ; Michael Bonitz |
| title_fullStr | Nonequilibrium Green's functions approach to inhomogeneous systems Karsten Balzer ; Michael Bonitz |
| title_full_unstemmed | Nonequilibrium Green's functions approach to inhomogeneous systems Karsten Balzer ; Michael Bonitz |
| title_short | Nonequilibrium Green's functions approach to inhomogeneous systems |
| title_sort | nonequilibrium green s functions approach to inhomogeneous systems |
| topic | Green-Funktion (DE-588)4158123-4 gnd Inhomogenes Medium (DE-588)4228459-4 gnd Nichtgleichgewicht (DE-588)4171730-2 gnd Quantenmechanisches System (DE-588)4300046-0 gnd |
| topic_facet | Green-Funktion Inhomogenes Medium Nichtgleichgewicht Quantenmechanisches System |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=4164605&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025495619&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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