Reduced density matrix functional theory at finite temperature

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1. Verfasser: Baldsiefen, Tim (VerfasserIn)
Format: Abschlussarbeit Buch
Sprache:English
Veröffentlicht: 2012
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Datensatz im Suchindex

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adam_text IMAGE 1 TABLE O F C O N T E N T S LIST O F F I G U R E S V LIST O F T A B L E S V I I LIST O F A B B R E V I A T I O N S I X 1 I N T R O D U C T I O N 1 2 M A T H E M A T I C A L P R E R E Q U I S I T E S 5 2.1 HAMILTONIAN AND SPIN NOTATION 5 2.2 STATISTICAL DENSITY OPERATOR (SDO) 5 2.3 1-REDUCED DENSITY MATRIX (1R.DM) 6 2.4 HOMOGENEOUS ELECTRON GAS (HEG) 8 3 Z E R O - T E M P E R A T U R E R D M F T 1 1 3.1 THEORETICAL FOUNDATIONS 11 3.1.1 EXCHANGE-CORRELATION FUNCTIONALS 13 3.2 THE PROBLEM OF THE CONSTRUCTION OF AN RDMFT-LDA 14 3.3 BOW FUNCTIONAL 16 3.4 THE PROBLEM OF THE DESCRIPTION OF MAGNETIC SYSTEMS 19 3.5 SUMMARY AND OUTLOOK 22 4 F I N I T E - T E M P E R A T U R E R D M F T ( F T - R D M F T ) 2 3 4.1 PHYSICAL SITUATION AND STANDARD QUANTUM MECHANICAL TREATMENT - 24 4.1.1 PROPERTIES OF THERMODYNAMIC VARIABLES 25 4.2 MATHEMATICAL FOUNDATION OF FT-RDMFT 27 4.2.1 EXISTENCE OF GRAND POTENTIAL FUNCTIONAL O[--/] 28 4.2.2 LIEB FORMULATION OF THE UNIVERSAL FUNCTIONAL 29 4.2.3 KOHN-SHAM SYSTEM FOR FT-RDMFT 31 4.2.4 FUNCTIONALS IN FT-RDMFT 31 4.2.5 FINITE-TEMPERATURE HARTREE-FOCK (FT-HF) 32 4.3 PROPERTIES OF THE UNIVERSAL FUNCTIONAL 33 4.3.1 EXISTENCE OF MINIMUM 33 4.3.2 LOWER SEMICONTINUITY 35 4.3.3 CONVEXITY 36 4.4 EQ-V-REPRESENTABILITY 36 4.5 RELATION TO MICROCANONICAL AND CANONICAL FORMULATIONS 38 4.6 SUMMARY AND OUTLOOK 40 5 P R O P E R T I E S O F T H E E X A C T F T - R D M F T F U N C T I O N A L S 4 3 5.1 NEGATIVITY OF THE CORRELATION FUNCTIONALS SL C . W C , S C 43 5.2 ADIABATIC CONNECTION FORMULA 44 5.3 UNIFORM COORDIANTE SCALING 45 5.4 TEMPERATURE AND INTERACTION SCALING 48 5.5 SUMMARY AND OUTLOOK 49 HTTP://D-NB.INFO/1032278935 IMAGE 2 TABLE OF CONTENTS 6 C O N S T R U C T I N G A P P R O X I M A T E F U N C T I O N A L S 5 1 6.1 WHY NOT USE STANDARD FT-MBPT? 51 6.2 METHODOLOGY OF MODIFIED PERTURBATION THEORY 53 6.2.1 ELIMINATION OF VGFJ 54 6.3 IMPORTANCE OF EQ-V-REPRESENTABILITY 58 6.4 . SCALING BEHAVIOUR 59 6.5 SUMMARY AND OUTLOOK 60 7 N U M E R I C A L T R E A T M E N T - 6 1 7.1 KEY IDEA OF SELF-CONSISTENT MINIMIZATION 61 7.2 EFFECTIVE HAMILTONIAN 63 7.3 TEMPERATURE TENSOR 64 7.4 SMALL STEP INVESTIGATION 66 7.4.1 OCCUPATION NUMBER (ON) CONTRIBUTION 68 7.4.2 NATURAL ORBITAL (NO) CONTRIBUTION 68 7.5 CONVERGENCE MEASURES 69 7.6 SAMPLE CALCULATIONS 0 7.6.1 OCCUPATION NUMBER (ON) MINIMIZATION 70 7.6.2 FULL MINIMIZATION 72 7.6.3 SUMMARY AND OUTLOOK 74 8 A P P L I C A T I O N S 7 5 8.1 MAGNETIC PHASE TRANSITIONS IN THE HEG 76 8.2 HOMOGENEOUS ELECTRON GAS WITH CONTACT INTERACTION 79 8.3 FT-MBPT 80 8.3.1 EXCHANGE-ONLY 81 8.3.2 EXCHANGE + RPA 83 8.3.3 EXCHANGE + RPA + SECOND-ORDER BORN 86 8.4 FT-RDMFT 88 8.4.1 COLLINEAR SPIN CONFIGURATION 89 8.4.2 PLANAR SPIN SPIRALS (PSS) 93 8.5 FT-HF DISPERSION RELATIONS 98 8.6 CORRELATION IN FT-RDMFT 100 8.6.1 DFT-LSDA CORRELATION 100 8.6.2 FT-DFT-RPA CORRELATION 102 8.6.3 ZERO-TEMPERATURE RDMFT CORRELATION 103 8.6.4 FT-RDMFT PERTURBATION EXPANSION 106 8.7 SUMMARY AND OUTLOOK 110 A A P P E N D I X 1 1 3 A.L PROBABILISTIC INTERPRETATION OF THE ONS OF THE 1RDM 113 A.2 EQUILIBRIUM ONS IN GENERAL SYSTEMS 114 A.3 ZERO-TEMPERATURE MAPPING BETWEEN POTENTIALS AND WAVEFUNCTIONS 115 A.4 NONINTERACTING GRAND CANONICAL EQUILIBRIUM 116 A.5 FEYNMAN RULES 118 A.6 SECOND-ORDER BORN DIAGRAM 119 B B I B L I O G R A P H Y 1 2 1 C D E U T S C H E K U R Z F A S S U N G 1 3 1 D P U B L I C A T I O N S 1 3 3 II IMAGE 3 TABLE OF CONTENTS E A C K N O W L E D G E M E N T S
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spellingShingle Baldsiefen, Tim
Reduced density matrix functional theory at finite temperature
subject_GND (DE-588)4113937-9
title Reduced density matrix functional theory at finite temperature
title_alt Reduzierte-Dichtematrix-Funktionaltheorie bei endlicher Temperatur
title_auth Reduced density matrix functional theory at finite temperature
title_exact_search Reduced density matrix functional theory at finite temperature
title_full Reduced density matrix functional theory at finite temperature vorgelegt von Tim Baldsiefen
title_fullStr Reduced density matrix functional theory at finite temperature vorgelegt von Tim Baldsiefen
title_full_unstemmed Reduced density matrix functional theory at finite temperature vorgelegt von Tim Baldsiefen
title_short Reduced density matrix functional theory at finite temperature
title_sort reduced density matrix functional theory at finite temperature
topic_facet Hochschulschrift
url http://www.diss.fu-berlin.de/diss/receive/FUDISS_thesis_000000040031
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