The flow equation approach to many particle systems:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin
Springer
2006
|
| Series: | Springer tracts in modern physics
217 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XII, 170 S. Ill., graph. Darst. |
| ISBN: | 9783540340676 354034067X |
Staff View
MARC
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| 100 | 1 | |a Kehrein, Stefan |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The flow equation approach to many particle systems |c Stefan Kehrein |
| 264 | 1 | |a Berlin |b Springer |c 2006 | |
| 300 | |a XII, 170 S. |b Ill., graph. Darst. | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
1 Introduction 1
1.1 Motivation 1
1.2 Flow Equations: Basic Ideas 2
1.3 Outline and Scope of this Book 7
References 9
2 Transformation of the Hamiltonian 11
2.1 Energy Scale Separation 11
2.1.1 Potential Scattering Model 12
2.1.2 Kondo Model 19
2.2 Flow Equation Approach 22
2.2.1 Motivation 22
2.2.2 Infinitesimal Unitary Transformations 23
2.2.3 Choice of Generator 25
2.2.4 Flow Equations 28
2.3 Example: Potential Scattering Model 31
2.3.1 Setting up the Flow Equations 31
2.3.2 Methods of Solution 34
2.3.3 Strong Coupling Case 39
References 40
3 Evaluation of Observables 43
3.1 Expectation Values 43
3.1.1 Zero Temperature 43
3.1.2 Nonzero Temperature 46
3.2 Correlation Functions 47
3.2.1 Zero Temperature 47
3.2.2 Nonzero Temperature 49
3.2.3 Fluctuation Dissipation Theorem 50
3.3 Examples 51
3.3.1 Potential Scattering Model 52
3.3.2 Resonant Level Model 54
References 61
XII Contents
4 Interacting Many Body Systems 63
4.1 Normal Ordering 63
4.1.1 Bosons 64
4.1.2 Fermions 69
4.1.3 Important Commutators 70
4.1.4 Normal Ordered Expansions 73
4.1.5 Normal Ordering with Respect to Which State? 77
4.2 Kondo Model 78
4.2.1 Expansion in 1st Order (1 Loop Results) 79
4.2.2 Expansion in 2nd Order (2 Loop Results) 83
4.2.3 Nonzero Temperature 88
4.2.4 Transformation of the Spin Operator 91
4.2.5 Spin Correlation Function and Dynamical
Susceptibility 95
4.2.6 Pseudogap Kondo Model 98
4.3 Spin Boson Model 102
4.3.1 Flow of the Hamiltonian 102
4.3.2 Low Energy Observables 107
4.3.3 Resonant Behavior 109
4.4 Interacting Fermions in d 1 Dimensions 113
4.4.1 Flow Equations and Fermi Liquid Theory 114
4.4.2 Flow Equations and Molecular Field
Type Hamiltonians 121
4.5 Other Applications 123
4.5.1 Construction of Effective Hamiltonians:
The Frohlich Transformation Re examined 124
4.5.2 Block Diagonal Hamiltonians 132
References 133
5 Modern Developments 137
5.1 Strong Coupling Behavior: Sine Gordon Model 137
5.1.1 Sine Gordon Model 138
5.1.2 Flow Equation Analysis 140
5.1.3 Conventional Scaling vs. Flow Equations 146
5.2 Steady Non Equilibrium: Kondo Model with Voltage Bias . . . 151
5.2.1 Kondo Model in Non Equilibrium 151
5.2.2 Flow Equation Analysis 153
5.2.3 Correlation Functions in Non Equilibrium:
Spin Dynamics 159
5.3 Real Time Evolution: Spin Boson Model 163
5.4 Outlook and Open Questions 167
References 168
Index 169
|
| adam_txt |
Contents
1 Introduction 1
1.1 Motivation 1
1.2 Flow Equations: Basic Ideas 2
1.3 Outline and Scope of this Book 7
References 9
2 Transformation of the Hamiltonian 11
2.1 Energy Scale Separation 11
2.1.1 Potential Scattering Model 12
2.1.2 Kondo Model 19
2.2 Flow Equation Approach 22
2.2.1 Motivation 22
2.2.2 Infinitesimal Unitary Transformations 23
2.2.3 Choice of Generator 25
2.2.4 Flow Equations 28
2.3 Example: Potential Scattering Model 31
2.3.1 Setting up the Flow Equations 31
2.3.2 Methods of Solution 34
2.3.3 Strong Coupling Case 39
References 40
3 Evaluation of Observables 43
3.1 Expectation Values 43
3.1.1 Zero Temperature 43
3.1.2 Nonzero Temperature 46
3.2 Correlation Functions 47
3.2.1 Zero Temperature 47
3.2.2 Nonzero Temperature 49
3.2.3 Fluctuation Dissipation Theorem 50
3.3 Examples 51
3.3.1 Potential Scattering Model 52
3.3.2 Resonant Level Model 54
References 61
XII Contents
4 Interacting Many Body Systems 63
4.1 Normal Ordering 63
4.1.1 Bosons 64
4.1.2 Fermions 69
4.1.3 Important Commutators 70
4.1.4 Normal Ordered Expansions 73
4.1.5 Normal Ordering with Respect to Which State? 77
4.2 Kondo Model 78
4.2.1 Expansion in 1st Order (1 Loop Results) 79
4.2.2 Expansion in 2nd Order (2 Loop Results) 83
4.2.3 Nonzero Temperature 88
4.2.4 Transformation of the Spin Operator 91
4.2.5 Spin Correlation Function and Dynamical
Susceptibility 95
4.2.6 Pseudogap Kondo Model 98
4.3 Spin Boson Model 102
4.3.1 Flow of the Hamiltonian 102
4.3.2 Low Energy Observables 107
4.3.3 Resonant Behavior 109
4.4 Interacting Fermions in d 1 Dimensions 113
4.4.1 Flow Equations and Fermi Liquid Theory 114
4.4.2 Flow Equations and Molecular Field
Type Hamiltonians 121
4.5 Other Applications 123
4.5.1 Construction of Effective Hamiltonians:
The Frohlich Transformation Re examined 124
4.5.2 Block Diagonal Hamiltonians 132
References 133
5 Modern Developments 137
5.1 Strong Coupling Behavior: Sine Gordon Model 137
5.1.1 Sine Gordon Model 138
5.1.2 Flow Equation Analysis 140
5.1.3 Conventional Scaling vs. Flow Equations 146
5.2 Steady Non Equilibrium: Kondo Model with Voltage Bias . . . 151
5.2.1 Kondo Model in Non Equilibrium 151
5.2.2 Flow Equation Analysis 153
5.2.3 Correlation Functions in Non Equilibrium:
Spin Dynamics 159
5.3 Real Time Evolution: Spin Boson Model 163
5.4 Outlook and Open Questions 167
References 168
Index 169 |
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| spelling | Kehrein, Stefan Verfasser aut The flow equation approach to many particle systems Stefan Kehrein Berlin Springer 2006 XII, 170 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer tracts in modern physics 217 Literaturangaben Condensed matter Hamiltonian systems Many-body problem Particles (Nuclear physics) Quantum field theory Unitary transformations Quantenmechanisches System (DE-588)4300046-0 gnd rswk-swf Berechnung (DE-588)4120997-7 gnd rswk-swf Vielteilchensystem (DE-588)4063491-7 gnd rswk-swf Festkörper (DE-588)4016918-2 gnd rswk-swf Festkörper (DE-588)4016918-2 s Quantenmechanisches System (DE-588)4300046-0 s Vielteilchensystem (DE-588)4063491-7 s Berechnung (DE-588)4120997-7 s DE-604 Springer tracts in modern physics 217 (DE-604)BV000000153 217 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2793079&prov=M&dok_var=1&dok_ext=htm Inhaltstext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016081264&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kehrein, Stefan The flow equation approach to many particle systems Springer tracts in modern physics Condensed matter Hamiltonian systems Many-body problem Particles (Nuclear physics) Quantum field theory Unitary transformations Quantenmechanisches System (DE-588)4300046-0 gnd Berechnung (DE-588)4120997-7 gnd Vielteilchensystem (DE-588)4063491-7 gnd Festkörper (DE-588)4016918-2 gnd |
| subject_GND | (DE-588)4300046-0 (DE-588)4120997-7 (DE-588)4063491-7 (DE-588)4016918-2 |
| title | The flow equation approach to many particle systems |
| title_auth | The flow equation approach to many particle systems |
| title_exact_search | The flow equation approach to many particle systems |
| title_exact_search_txtP | The flow equation approach to many particle systems |
| title_full | The flow equation approach to many particle systems Stefan Kehrein |
| title_fullStr | The flow equation approach to many particle systems Stefan Kehrein |
| title_full_unstemmed | The flow equation approach to many particle systems Stefan Kehrein |
| title_short | The flow equation approach to many particle systems |
| title_sort | the flow equation approach to many particle systems |
| topic | Condensed matter Hamiltonian systems Many-body problem Particles (Nuclear physics) Quantum field theory Unitary transformations Quantenmechanisches System (DE-588)4300046-0 gnd Berechnung (DE-588)4120997-7 gnd Vielteilchensystem (DE-588)4063491-7 gnd Festkörper (DE-588)4016918-2 gnd |
| topic_facet | Condensed matter Hamiltonian systems Many-body problem Particles (Nuclear physics) Quantum field theory Unitary transformations Quantenmechanisches System Berechnung Vielteilchensystem Festkörper |
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