Functional renormalization and ultracold quantum gases:
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| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Heidelberg [u.a.]
Springer
2010
|
| Series: | Springer Theses
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | IX, 199 S. graph. Darst. |
| ISBN: | 9783642141126 |
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Record in the Search Index
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CONTENTS 1 INTRODUCTION 1 1.1 FLOW EQUATIONS TO SOLVE AN INTEGRAL 4 1.2
FUNCTIONAL INTEGRAL REPRESENTATION OF QUANTUM FIELD THEORY . 8 1.2.1
FROM THE LATTICE TO FIELD THEORY 9 1.2.2 EXPECTATION VALUES, CORRELATION
FUNCTIONS 10 1.2.3 FUNCTIONAL DERIVATIVES, GENERATING FUNCTIONALS 11
1.2.4 MICROSCOPIC ACTIONS IN REAL TIME AND ANALYTIC CONTINUATION 13
1.2.5 MATSUBARA FORMALISM 14 REFERENCES 15 2 THE WETTERICH EQUATION 17
2.1 SCALE DEPENDENT SCHWINGER FUNCTIONAL 17 2.2 THE AVERAGE ACTION AND
ITS FLOW EQUATION 19 2.3 FUNCTIONAL INTEGRAL REPRESENTATION AND INITIAL
CONDITION 20 REFERENCE 21 3 GENERALIZED FLOW EQUATION 23 3.1
SCALE-DEPENDENT BOSONIZATION 23 3.2 FLOWING ACTION 27 3.3 GENERAL
COORDINATE TRANSFORMATIONS 29 REFERENCES 31 4 TRUNCATIONS 33 4.1
SYMMETRIES AS A GUIDING PRINCIPLES 34 4.2 SEPARATION OF SCALES 35 4.3
DERIVATIVE EXPANSION 36 5 CUTOFF CHOICES 39 REFERENCES 42
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1002961815 DIGITALISIERT
DURCH VIII CONTENTS 6 INVESTIGATED MODELS 43 6. 1 BOSE GAS IN THREE
DIMENSIONS 43 6.1.1 LAGRANGIAN 44 6.2 BOSE GAS IN TWO DIMENSIONS 46 6.3
BCS-BEC CROSSOVER 48 6.3.1 LAGRANGIAN 51 6.4 BCS-TRION-BEC TRANSITION 52
6.4.1 LAGRANGIAN 53 REFERENCES 54 7 SYMMETRIES 59 7.1 DERIVATIVE
EXPANSION AND WARD IDENTITIES 59 7.1.1 PROPAGATOR AND DISPERSION 63 7.2
NOETHERS THEOREM 65 REFERENCES 69 8 TRUNCATED FLOW EQUATIONS 71 8.1 BOSE
GAS 71 8.1.1 FLOW EQUATIONS FOR THE EFFECTIVE POTENTIAL 73 8.1.2 KINETIC
COEFFICIENTS 76 8.2 BCS-BEC CROSSOVER 78 8.2.1 FLOW OF THE EFFECTIVE
POTENTIAL 79 8.3 BCS-TRION-BEC TRANSITION 82 REFERENCES 83 9 FEW-BODY
PHYSICS 85 9.1 REPULSIVE INTERACTING BOSONS 86 9.1.1 VACUUM FLOW
EQUATIONS AND THEIR SOLUTION FOR D = 3 . . . 86 9.1.2 LOGARITHMIC
RUNNING IN TWO DIMENSIONS 89 9.2 TWO FERMION SPECIES: DIMER FORMATION 91
9.2.1 TWO-BODY PROBLEM 92 9.2.2 RENORMALIZATION 93 9.2.3 BINDING ENERGY
95 9.2.4 DIMER-DIMER SCATTERING 96 9.3 THREE FERMION SPECIES: EFIMOV
EFFECT 97 9.3.1 SU(3) SYMMETRIC MODEL 98 9.3.2 EXPERIMENTS WITH LITHIUM
107 REFERENCES 115 10 MANY-BODY PHYSICS 11 CONTENTS IX 10.1.4 THERMAL
DEPLETION OF CONDENSATE 123 10.1.5 CRITICAL TEMPERATURE 126 10.1.6 ZERO
TEMPERATURE SOUND VELOCITY 127 10.1.7 THERMODYNAMIC OBSERVABLES 129 10.2
SUPERFLUID BOSE GAS IN TWO DIMENSIONS 144 10.2.1 FLOW EQUATIONS AT ZERO
TEMPERATURE 144 10.2.2 QUANTUM DEPLETION OF CONDENSATE 146 10.2.3
DISPERSION RELATION AND SOUND VELOCITY 147 10.2.4 KOSTERLITZ-THOULESS
PHYSICS 149 10.3 PARTICLE-HOLE FLUCTUATIONS AND THE BCS-BEC CROSSOVER
154 10.3.1 PARTICLE-HOLE FLUCTUATIONS 154 10.3.2 BOSONIZATION 157 10.3.3
CRITICAL TEMPERATURE 161 10.3.4 PHASE DIAGRAM 162 10.3.5 CROSSOVER TO
NARROW RESONANCES 164 10.4 BCS-TRION-BEC TRANSITION 166 REFERENCES 168
11 CONCLUSIONS 171 REFERENCES 175 12 APPENDICES 177 12.1 APPENDIX A:
SOME IDEAS ON FUNCTIONAL INTEGRATION AND PROBABILITY 177 12.1.1
FUNCTIONAL INTEGRAL WITH PROBABILITY MEASURE 178 12.1.2 CORRELATION
FUNCTIONS FROM FUNCTIONAL PROBABILITIES . 184 12.1.3 CONSERVATION
LAWS FOR ON-SHELL EXCITATIONS 187 12.1.4 CONCLUSIONS 188 12.2 APPENDIX
B: TECHNICAL ADDITIONS 189 12.2.1 FLOW OF THE EFFECTIVE POTENTIAL FOR
BOSE GAS 189 12.2.2 FLOW OF THE EFFECTIVE POTENTIAL FOR BCS-BEC
CROSSOVER 191 12.2.3 HIERARCHY OF FLOW EQUATIONS IN VACUUM 196
REFERENCES 199 |
| any_adam_object | 1 |
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| author_GND | (DE-588)138826374 |
| author_facet | Flörchinger, Stefan 1982- |
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| dewey-full | 530.143 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.143 |
| dewey-search | 530.143 |
| dewey-sort | 3530.143 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Thesis Book |
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| isbn | 9783642141126 |
| language | English |
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| physical | IX, 199 S. graph. Darst. |
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| spelling | Flörchinger, Stefan 1982- Verfasser (DE-588)138826374 aut Functional renormalization and ultracold quantum gases Stefan Flörchinger Heidelberg [u.a.] Springer 2010 IX, 199 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer Theses Zugl.: Heidelberg, Univ., Diss., 2009 Renormierung (DE-588)4128419-7 gnd rswk-swf Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf Quantengas (DE-588)4755839-8 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Quantengas (DE-588)4755839-8 s Quantenfeldtheorie (DE-588)4047984-5 s Renormierung (DE-588)4128419-7 s DE-604 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3484447&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=020655601&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Flörchinger, Stefan 1982- Functional renormalization and ultracold quantum gases Renormierung (DE-588)4128419-7 gnd Quantenfeldtheorie (DE-588)4047984-5 gnd Quantengas (DE-588)4755839-8 gnd |
| subject_GND | (DE-588)4128419-7 (DE-588)4047984-5 (DE-588)4755839-8 (DE-588)4113937-9 |
| title | Functional renormalization and ultracold quantum gases |
| title_auth | Functional renormalization and ultracold quantum gases |
| title_exact_search | Functional renormalization and ultracold quantum gases |
| title_full | Functional renormalization and ultracold quantum gases Stefan Flörchinger |
| title_fullStr | Functional renormalization and ultracold quantum gases Stefan Flörchinger |
| title_full_unstemmed | Functional renormalization and ultracold quantum gases Stefan Flörchinger |
| title_short | Functional renormalization and ultracold quantum gases |
| title_sort | functional renormalization and ultracold quantum gases |
| topic | Renormierung (DE-588)4128419-7 gnd Quantenfeldtheorie (DE-588)4047984-5 gnd Quantengas (DE-588)4755839-8 gnd |
| topic_facet | Renormierung Quantenfeldtheorie Quantengas Hochschulschrift |
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