Topics and methods in condensed matter theory: from basic quantum mechanics to the frontiers of research
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| Format: | Book |
| Language: | English |
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Berlin [u.a.]
Springer
2007
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| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XVII, 443 S. Ill., graph. Dast. |
| ISBN: | 9783540707264 3540707263 |
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| 245 | 1 | 0 | |a Topics and methods in condensed matter theory |b from basic quantum mechanics to the frontiers of research |c Michele Cini |
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MICHELE CINI TOPICS AND METHODS IN CONDENSED MATTER THEORY FROM BASIC
QUANTUM MECHANICS TO THE FRONTIERS OF RESEARCH WITH 73 FIGURES AND 4
TABLES 4Y SPRINGER CONTENTS PART I I-INTRODUCTORY MANY-BODY PHYSICS
BASIC MANY-BODY QUANTUM MECHANICS 1 1.1 SLATER DETERMINANTS AND MATRIX
ELEMENTS 1 1.1.1 MANY-ELECTRON MATRIX ELEMENTS 2 1.1.2 DERIVATION OF THE
RULES 4 1.2 SECOND QUANTIZATION 5 1.2.1 BOSONS 5 1.2.2 FIELD
QUANTIZATION AND CASIMIR EFFECT 7 1.2.3 FERMIONS 9 1.2.4 BASIS CHANGE IN
SECOND QUANTIZATION AND FIELD OPERATORS 11 1.2.5 HUBBARD MODEL FOR THE
HYDROGEN MOLECULE 13 1.3 SCHRIEFFER-WOLFF CANONICAL TRANSFORMATION 15
1.4 VARIATIONAL PRINCIPLE 16 1.5 VARIATIONAL APPROXIMATIONS 18 1.6
NON-DEGENERATE PERTURBATION THEORY 18 ADIABATIC SWITCHING AND
TIME-ORDERED SERIES 19 2.1 TIME-DEPENDENT IS BETTER: START FROM THE
GOLDEN AGE 19 2.2 EVOLUTION IN COMPLEX TIME 21 2.2.1 HEISENBERG PICTURE
21 2.2.2 THERMAL AVERAGES 23 2.3 THE INTERACTION PICTURE AND THE VIABLE
EXPANSION 25 PROBLEMS 26 ATOMIC SHELLS AND MULTIPLETS 29 3.1 SHELL
STRUCTURE OF ATOMS T 29 3.2 HARTREE-FOCK METHOD 29 3.2.1 PHYSICAL
MEANING OF EXCHANGE: THE COHESION OF A SIMPLE METAL 35 3.3 VIRIAL
THEOREM 37 3.4 HELLMANN-FEYNMAN THEOREM 38 3.5 CENTRAL FIELD_ 38 3.5.1
L-S MULTIPLETS {H' REL - 0 LIMIT) 40 XII CONTENTS 3.5.2 HUND'S FIRST
RULE 42 3.6 ATOMIC COULOMB INTEGRALS 43 3.6.1 HUND'S SECOND RULE 46
3.6.2 J-J COUPLING 46 3.6.3 INTERMEDIATE COUPLING 46 3.7 MEITNER-AUGER
EFFECT AND SPECTROSCOPY 48 3.7.1 AUGER SELECTION RULES AND LINE
INTENSITIES 50 4 GREEN'S FUNCTIONS AS THOUGHT EXPERIMENTS 55 4.1 GREEN'S
THEOREM FOR ONE-BODY PROBLEMS 55 4.2 HOW MANY-BODY GREEN'S FUNCTIONS
ARISE 55 4.2.1 CORRELATION FUNCTIONS 55 4.2.2 QUANTUM GREEN'S FUNCTIONS
57 4.2.3 QUANTUM AVERAGES 58 4.2.4 GREEN'S FUNCTIONS AT FINITE
TEMPERATURE 59 4.3 NON-INTERACTING PROPAGATORS FOR SOLIDS 61 4.3.1
GREEN'S FUNCTIONS FOR TIGHT-BINDING HAMILTONIANS . 66 4.3.2
LIPPMANN-SCHWINGER EQUATION 70 4.3.3 T MATRIX ,;.:. 70 4.3.4 INGLESFIELD
EMBEDDING METHOD 71 4.4 KUBO FORMULAE 73 4.5 VACUUM AMPLITUDES 75 4.6
LEHMANN REPRESENTATION 76 4.6.1 ZERO-TEMPERATURE FERMI CASE 76 4.6.2
FINITE TEMPERATURES, FERMI AND BOSE 78 4.6.3 FLUCTUATION-DISSIPATION
THEOREM 79 5 HOPPING ELECTRON MODELS: AN APPETIZER 81 5.1 FANO
RESONANCES AND RESOLVENTS 81 5.1.1 RESONANCES 81 5.1.2 FANO MODEL 82
5.1.3 ONE-BODY TREATMENT 82 5.1.4 MANY-BODY TREATMENT 83 5.1.5 THE
RESOLVENT 86 5.1.6 SELF-ENERGY OPERATOR 89 5.2 MAGNETIC IMPURITIES AND
CHEMISORPTION ON TRANSITION METAL SURFACES A-. 90 5.3 STRONG COUPLING
AND THE KONDO PEAK 95 5.3.1 NARROW-BAND ANDERSON MODEL 95 5.3.2 ANDERSON
MODEL, S-D MODEL AND KONDO MODEL 98 5.3.3 FERMI LEVEL SINGULARITY AND
KONDO MINIMUM 100 5.4 THE N F » 1 EXPANSION 101 5.4.1 KONDO TEMPERATURE
IN THE SPIN-FLUCTUATION CASE . 105 5.4.2 DENSITY OF OCCUPIED STATES
106 PROBLEMS 107 CONTENTS XIII 6 MANY-BODY EFFECTS IN ELECTRON
SPECTROSCOPIES 109 6.1 ELECTRON SPECTROSCOPY FOR CHEMICAL ANALYSIS
(ESCA) 109 6.1.1 CHEMICAL SHIFTS ILL 6.1.2 CORE-LEVEL SPLITTING IN
PARAMAGNETIC MOLECULES ILL 6.1.3 SHAKE-UP, SHAKE-OFF, RELAXATION 113
6.1.4 LUNDQVIST MODEL OF PHONON AND PLASMON SATELLITES . . . 115 6.2
AUGER CVV LINE SHAPES: TWO-HOLE RESONANCES 118 6.2.1 DESORPTION V . 122
6.3 TWO INTERACTING FERMIONS IN A LATTICE 123 6.4 QUADRATIC RESPONSE
FORMALISM AND SPECTROSCOPIES 127 6.4.1 ONE-STEP THEORY OF AUGER SPECTRA
129 6.4.2 PLASMON GAIN 130 PROBLEMS 130 PART II SYMMETRY IN QUANTUM
PHYSICS 7 GROUP REPRESENTATIONS FOR PHYSICISTS 133 7.1 ABSTRACT GROUPS
133 7.2 POINT SYMMETRY IN MOLECULES AND SOLIDS 135 7.2.1 SYMMETRY
OPERATORS 135 7.2.2 DIRAC CHARACTERS AND IRREDUCIBLE REPRESENTATIONS 140
7.2.3 SCHUR'S LEMMA 143 7.2.4 CONTINUOUS GROUPS 144 7.3 ACCIDENTAL
DEGENERACY AND HIDDEN SYMMETRIES 145 7.4 GREAT ORTHOGONALITY THEOREM
(GOT) 149 7.5 LITTLE ORTHOGONALITY THEOREM (LOT) 152 7.6 PROJECTION
OPERATORS 154 7.7 REGULAR REPRESENTATION 155 PROBLEMS 156 8 SIMPLER USES
OF GROUP THEORY 157 8.1 MOLECULAR ORBITALS 157 8.1.1 MOLECULAR ORBITALS
OF NH 3 157 8.1.2 MOLECULAR ORBITALS OF CH A 158 8.1.3 CHARACTERS OF
ANGULAR MOMENTUM EIGENSTATES 160 8.1.4 EXAMPLES: OH GROUP, LIGAND GROUP
ORBITALS, CRYSTAL FIELD .*: 160 8.2 NORMAL MODES OF VIBRATION 163 8.3
SPACE-TIME SYMMETRIES OF BLOCH STATES 169 8.4 SPACE GROUPS OF SOLIDS 173
8.4.1 SYMMORPHIC AND NONSYMMORPHIC GROUPS 174 8.5 YOUNG DIAGRAMS 177
PROBLEMS 179 XIV CONTENTS 9 PRODUCT OF REPRESENTATIONS AND FURTHER
PHYSICAL APPLICATIONS 181 9.1 IRREDUCIBLE TENSOR OPERATORS 181 9.2
DIRECT PRODUCT REPRESENTATION 183 9.2.1 SELECTION RULES 184 9.3
REDUCTION OF THE DIRECT PRODUCT REPRESENTATION 185 9.4 SPIN-ORBIT
INTERACTION AND DOUBLE GROUPS 186 9.5 STATIC AND DYNAMICAL JAHN-TELLER
EFFECT 188 9.5.1 THE BORN-OPPENHEIMER (BO) APPROXIMATION 188 9.5.2 THE
JAHN-TELLER THEOREM 189 9.6 NON-ADIABATIC OPERATOR 193 9.6.1 DYNAMICAL
JAHN-TELLER EFFECT 194 9.6.2 HOW THE E X E HAMILTONIAN ARISES 196 9.6.3
NUCLEAR WAVE FUNCTIONS CANNOT BE TAKEN REAL 197 9.7 WIGNER-ECKART
THEOREM WITH APPLICATIONS 197 9.8 THE SYMMETRIC GROUP AND MANY-ELECTRON
STATES 199 9.9 SENIORITY NUMBERS IN ATOMIC PHYSICS 201 PROBLEMS 204 PART
III MORE ON GREEN FUNCTION TECHNIQUES 10 EQUATIONS OF MOTION AND FURTHER
DEVELOPMENTS 207 10.1 EQUATIONS OF MOTION FOR THE INTERACTING PROPAGATOR
207 10.1.1 EQUATIONS OF MOTION AND GROUND-STATE ENERGY 208 10.2
TIME-DEPENDENT PROBLEMS.: 208 10.2.1 AUGER INDUCED IONIC DESORPTION:
KNOTEK-FEIBELMAN MECHANISM 210 10.3 HIERARCHY OF GREENS FUNCTIONS 212
10.4 COMPOSITE OPERATOR METHOD 213 PROBLEMS 216 11 FEYNMAN DIAGRAMS FOR
CONDENSED MATTER PHYSICS 217 11.1 DIAGRAMS FOR THE VACUUM PROPAGATOR 217
11.1.1 WICK'S THEOREM 219 11.1.2 GOLDSTONE DIAGRAMS 221 11.1.3 DIAGRAM
RULES FOR THE THERMODYNASNIC POTENTIAL 224 11.2 LINKED CLUSTER THEOREM
225 11.2.1 VALENCE ELECTRON AND CORE HOLE 227 11.2.2 H 2 MODEL 229
11.2.3 THE LINKED CLUSTER EXPANSION AND GREEN'S FUNCTIONS . 230 11.3
DIAGRAMS FOR THE DRESSED PROPAGATOR 231 11.3.1 ADIABATIC SWITCHING AND
PERTURBATION THEORY 232 11.3.2 DIAGRAMS FOR THE PROPAGATOR IN FREQUENCY
SPACE 235 11.4 DYSON EQUATION 238 CONTENTS XV 11.4.1 EXTERNAL POTENTIAL
241 11.5 SELF-ENERGY FROM INTERACTIONS 242 11.6 SKELETON DIAGRAMS 245
11.7 TWO-BODY GREEN'S FUNCTION: THE BETHE-SALPETER EQUATION . 245 11.8
SELF-ENERGY AND TWO-BODY GREEN'S FUNCTION 247 11.9 FUNCTIONAL CALCULUS
AND DIAGRAMS 248 11.9.1 THE SELF-ENERGY AS A FUNCTIONAL 249 11.9.2
POLARIZATION BUBBLE : 251 11.9.3 THE VERTEX 253 11.10 HEDIN'S EQUATIONS
254 12 MANY-BODY EFFECTS AND FURTHER THEORY 257 12.1 HIGH DENSITY
ELECTRON GAS 257 12.1.1 MORE PHYSICAL INSIGHT ABOUT THE RPA 259 12.2 LOW
DENSITY ELECTRON GAS: LADDER APPROXIMATION 263 12.3 LADDER
APPROXIMATIONS IN ELECTRON SPECTROSCOPIES 264 12.3.1 XPS AND AUGER
SPECTRA FROM METALS 264 12.3.2 THE U 0 PHENOMENON 267 12.3.3 CORRELATION
IN EARLY TRANSITION METALS 270 12.4 CONSERVING APPROXIMATIONS 272 12.4.1
CONTINUITY EQUATION 272 12.4.2 THE $ FUNCTIONAL 274 12.4.3 GAUGE
TRANSFORMATION 275 12.4.4 GROUND-STATE ENERGY AND GRAND POTENTIAL 276
12.4.5 LUTTINGER-WARD AND ABL VARIATIONAL PRINCIPLES 277 12.5
GENERALIZED WARD IDENTITIES 278 12.6 CONNECTION OF DIAGRAMS TO D F T 279
12.6.1 HIGHLIGHTS ON DENSITY FUNCTIONAL THEORY 279 12.6.2 SHAM -
SCHLUTER EQUATION 282 PROBLEMS 283 13 NON-EQUILIBRIUM THEORY 285 13.1
TIME-DEPENDENT PROBES AND NONLINEAR RESPONSE 285 13.2 KADANOFF-BAYM AND
KELDYSH METHODS ; 286 13.3 COMPLEX-TIME INTEGRALS BY LANGRETH'S
TECHNIQUE 288 13.3.1 FINITE TEMPERATURES 290 13.4 KELDYSH-DYSON EQUATION
ON THE CONTOUR 291 13.5 EVOLUTION ON KELDYSH CONTOUR T 294 13.5.1
CONTOUR EVOLUTION OF BOSONS 298 13.6 SELECTED APPLICATIONS OF THE
KELDYSH FORMALISM 298 13.6.1 ATOM-SURFACE SCATTERING 299 13.6.2 QUANTUM
TRANSPORT 304 PROBLEMS 309 XVI CONTENTS PART IV NON-PERTURBATIVE
APPROACHES AND APPLICATIONS 14 SOME RECURSION TECHNIQUES WITH
APPLICATIONS 313 14.1 LANCZOS-HAYDOCK RECURSION 313 14.1.1 LOCAL GREEN'S
FUNCTION FOR A CHAIN 313 14.1.2 GREEN'S FUNCTION OF ANY SYSTEM^. 315
14.1.3 TERMINATOR 316 14.1.4 MOMENTS 322 14.2 SPIN-DISENTANGLED
DIAGONALIZATION 323 14.3 METHOD OF EXCITATION AMPLITUDES 326 14.4
FEENBERG METHOD 329 14.4.1 SOLVING LINEAR SYSTEMS 332 14.4.2 HOMOGENEOUS
SYSTEMS 333 PROBLEMS' 333 15 ASPECTS OF NONLINEAR OPTICS AND MANY-PHOTON
EFFECTS . 335 15.1 DIFFUSION OF RADIATION IN DIPOLE APPROXIMATION 335
15.1.1 SECOND-ORDER PROCESSES 336 15.2 SUM FREQUENCY AND SECOND-HARMONIC
GENERATION (SHG) . 342 15.3 DIFFUSION OF COHERENT LIGHT 343 15.3.1
EFFECTIVE MODE .' 343 15.3.2 DYNAMICAL STARK EFFECT 346 PROBLEMS '. 351
PART V SELECTED EXACT RESULTS IN MANY-BODY PROBLEMS 16 QUANTUM PHASES !
355 16.0.3 GAUGE TRANSFORMATIONS 355 16.0.4 SPINOR ROTATIONS 356 16.0.5
GALILEAN TRANSFORMATIONS 356 16.1 TOPOLOGIC PHASES 357 16.1.1 PARAMETRIC
HAMILTONIANS AND BERRY PHASE 358 16.1.2 POLARIZATION OF SOLIDS 362 17
PAIRING FROM REPULSIVE INTERACTIONS 17.0.3 W = 0 PAIRING IN CU-0
CLUSTERS 369 17.0.4 PAIRING MECHANISM 373 17.0.5 THE W = 0 THEOREM 373
17.0.6 EXAMPLES 375 17.1 SUPERCONDUCTING FLUX QUANTIZATION AND JOSEPHSON
EFFECT 378 PROBLEMS 381 CONTENTS XVII 18 ALGEBRAIC METHODS 383 18.1 LIEB
THEOREMS ON THE HALF FILLED HUBBARD MODEL 383 18.2 BETHE ANSATZ FOR THE
HEISENBERG CHAIN 387 18.3 BETHE ANSATZ FOR INTERACTING FERMIONS 1
DIMENSION 392 18.3.1 5- FUNCTION INTERACTION 392 18.3.2 THE HUBBARD
MODEL IN ID 396 18.3.3 THE PERIODIC BOUNDARY CONDITIONS 401 18.3.4 SPIN
CHAIN ANALOGY -: 403 PROBLEMS 406 PART VI APPENDICES 19 APPENDIX 1:
ZERO-POINT ENERGY IN A PILLBOX 409 20 APPENDIX II-CHARACTER TABLES 411
21 PROOF OF THE WIGNER-ECKART THEOREM 413 SOLUTIONS 415 REFERENCES 431
INDEX 439 |
| adam_txt |
MICHELE CINI TOPICS AND METHODS IN CONDENSED MATTER THEORY FROM BASIC
QUANTUM MECHANICS TO THE FRONTIERS OF RESEARCH WITH 73 FIGURES AND 4
TABLES 4Y SPRINGER CONTENTS PART I I-INTRODUCTORY MANY-BODY PHYSICS
BASIC MANY-BODY QUANTUM MECHANICS 1 1.1 SLATER DETERMINANTS AND MATRIX
ELEMENTS 1 1.1.1 MANY-ELECTRON MATRIX ELEMENTS 2 1.1.2 DERIVATION OF THE
RULES 4 1.2 SECOND QUANTIZATION 5 1.2.1 BOSONS 5 1.2.2 FIELD
QUANTIZATION AND CASIMIR EFFECT 7 1.2.3 FERMIONS 9 1.2.4 BASIS CHANGE IN
SECOND QUANTIZATION AND FIELD OPERATORS 11 1.2.5 HUBBARD MODEL FOR THE
HYDROGEN MOLECULE 13 1.3 SCHRIEFFER-WOLFF CANONICAL TRANSFORMATION 15
1.4 VARIATIONAL PRINCIPLE 16 1.5 VARIATIONAL APPROXIMATIONS 18 1.6
NON-DEGENERATE PERTURBATION THEORY 18 ADIABATIC SWITCHING AND
TIME-ORDERED SERIES 19 2.1 TIME-DEPENDENT IS BETTER: START FROM THE
GOLDEN AGE 19 2.2 EVOLUTION IN COMPLEX TIME 21 2.2.1 HEISENBERG PICTURE
21 2.2.2 THERMAL AVERAGES 23 2.3 THE INTERACTION PICTURE AND THE VIABLE
EXPANSION 25 PROBLEMS 26 ATOMIC SHELLS AND MULTIPLETS 29 3.1 SHELL
STRUCTURE OF ATOMS T 29 3.2 HARTREE-FOCK METHOD 29 3.2.1 PHYSICAL
MEANING OF EXCHANGE: THE COHESION OF A SIMPLE METAL 35 3.3 VIRIAL
THEOREM 37 3.4 HELLMANN-FEYNMAN THEOREM 38 3.5 CENTRAL FIELD_ 38 3.5.1
L-S MULTIPLETS {H' REL - 0 LIMIT) 40 XII CONTENTS 3.5.2 HUND'S FIRST
RULE 42 3.6 ATOMIC COULOMB INTEGRALS 43 3.6.1 HUND'S SECOND RULE 46
3.6.2 J-J COUPLING 46 3.6.3 INTERMEDIATE COUPLING 46 3.7 MEITNER-AUGER
EFFECT AND SPECTROSCOPY 48 3.7.1 AUGER SELECTION RULES AND LINE
INTENSITIES 50 4 GREEN'S FUNCTIONS AS THOUGHT EXPERIMENTS 55 4.1 GREEN'S
THEOREM FOR ONE-BODY PROBLEMS 55 4.2 HOW MANY-BODY GREEN'S FUNCTIONS
ARISE 55 4.2.1 CORRELATION FUNCTIONS 55 4.2.2 QUANTUM GREEN'S FUNCTIONS
57 4.2.3 QUANTUM AVERAGES 58 4.2.4 GREEN'S FUNCTIONS AT FINITE
TEMPERATURE 59 4.3 NON-INTERACTING PROPAGATORS FOR SOLIDS 61 4.3.1
GREEN'S FUNCTIONS FOR TIGHT-BINDING HAMILTONIANS . 66 4.3.2
LIPPMANN-SCHWINGER EQUATION 70 4.3.3 T MATRIX ,;.:. 70 4.3.4 INGLESFIELD
EMBEDDING METHOD 71 4.4 KUBO FORMULAE 73 4.5 VACUUM AMPLITUDES 75 4.6
LEHMANN REPRESENTATION 76 4.6.1 ZERO-TEMPERATURE FERMI CASE 76 4.6.2
FINITE TEMPERATURES, FERMI AND BOSE 78 4.6.3 FLUCTUATION-DISSIPATION
THEOREM 79 5 HOPPING ELECTRON MODELS: AN APPETIZER 81 5.1 FANO
RESONANCES AND RESOLVENTS 81 5.1.1 RESONANCES 81 5.1.2 FANO MODEL 82
5.1.3 ONE-BODY TREATMENT 82 5.1.4 MANY-BODY TREATMENT 83 5.1.5 THE
RESOLVENT 86 5.1.6 SELF-ENERGY OPERATOR 89 5.2 MAGNETIC IMPURITIES AND
CHEMISORPTION ON TRANSITION METAL SURFACES A-. 90 5.3 STRONG COUPLING
AND THE KONDO PEAK 95 5.3.1 NARROW-BAND ANDERSON MODEL 95 5.3.2 ANDERSON
MODEL, S-D MODEL AND KONDO MODEL 98 5.3.3 FERMI LEVEL SINGULARITY AND
KONDO MINIMUM 100 5.4 THE N F » 1 EXPANSION 101 5.4.1 KONDO TEMPERATURE
IN THE SPIN-FLUCTUATION CASE . 105 5.4.2 DENSITY OF OCCUPIED STATES
106 PROBLEMS 107 CONTENTS XIII 6 MANY-BODY EFFECTS IN ELECTRON
SPECTROSCOPIES 109 6.1 ELECTRON SPECTROSCOPY FOR CHEMICAL ANALYSIS
(ESCA) 109 6.1.1 CHEMICAL SHIFTS ILL 6.1.2 CORE-LEVEL SPLITTING IN
PARAMAGNETIC MOLECULES ILL 6.1.3 SHAKE-UP, SHAKE-OFF, RELAXATION 113
6.1.4 LUNDQVIST MODEL OF PHONON AND PLASMON SATELLITES . . . 115 6.2
AUGER CVV LINE SHAPES: TWO-HOLE RESONANCES 118 6.2.1 DESORPTION V . 122
6.3 TWO INTERACTING FERMIONS IN A LATTICE 123 6.4 QUADRATIC RESPONSE
FORMALISM AND SPECTROSCOPIES 127 6.4.1 ONE-STEP THEORY OF AUGER SPECTRA
129 6.4.2 PLASMON GAIN 130 PROBLEMS 130 PART II SYMMETRY IN QUANTUM
PHYSICS 7 GROUP REPRESENTATIONS FOR PHYSICISTS 133 7.1 ABSTRACT GROUPS
133 7.2 POINT SYMMETRY IN MOLECULES AND SOLIDS 135 7.2.1 SYMMETRY
OPERATORS 135 7.2.2 DIRAC CHARACTERS AND IRREDUCIBLE REPRESENTATIONS 140
7.2.3 SCHUR'S LEMMA 143 7.2.4 CONTINUOUS GROUPS 144 7.3 ACCIDENTAL
DEGENERACY AND HIDDEN SYMMETRIES 145 7.4 GREAT ORTHOGONALITY THEOREM
(GOT) 149 7.5 LITTLE ORTHOGONALITY THEOREM (LOT) 152 7.6 PROJECTION
OPERATORS 154 7.7 REGULAR REPRESENTATION 155 PROBLEMS 156 8 SIMPLER USES
OF GROUP THEORY 157 8.1 MOLECULAR ORBITALS 157 8.1.1 MOLECULAR ORBITALS
OF NH 3 157 8.1.2 MOLECULAR ORBITALS OF CH A 158 8.1.3 CHARACTERS OF
ANGULAR MOMENTUM EIGENSTATES 160 8.1.4 EXAMPLES: OH GROUP, LIGAND GROUP
ORBITALS, CRYSTAL FIELD .*: 160 8.2 NORMAL MODES OF VIBRATION 163 8.3
SPACE-TIME SYMMETRIES OF BLOCH STATES 169 8.4 SPACE GROUPS OF SOLIDS 173
8.4.1 SYMMORPHIC AND NONSYMMORPHIC GROUPS 174 8.5 YOUNG DIAGRAMS 177
PROBLEMS 179 XIV CONTENTS 9 PRODUCT OF REPRESENTATIONS AND FURTHER
PHYSICAL APPLICATIONS 181 9.1 IRREDUCIBLE TENSOR OPERATORS 181 9.2
DIRECT PRODUCT REPRESENTATION 183 9.2.1 SELECTION RULES 184 9.3
REDUCTION OF THE DIRECT PRODUCT REPRESENTATION 185 9.4 SPIN-ORBIT
INTERACTION AND DOUBLE GROUPS 186 9.5 STATIC AND DYNAMICAL JAHN-TELLER
EFFECT 188 9.5.1 THE BORN-OPPENHEIMER (BO) APPROXIMATION 188 9.5.2 THE
JAHN-TELLER THEOREM 189 9.6 NON-ADIABATIC OPERATOR 193 9.6.1 DYNAMICAL
JAHN-TELLER EFFECT 194 9.6.2 HOW THE E X E HAMILTONIAN ARISES 196 9.6.3
NUCLEAR WAVE FUNCTIONS CANNOT BE TAKEN REAL 197 9.7 WIGNER-ECKART
THEOREM WITH APPLICATIONS 197 9.8 THE SYMMETRIC GROUP AND MANY-ELECTRON
STATES 199 9.9 SENIORITY NUMBERS IN ATOMIC PHYSICS 201 PROBLEMS 204 PART
III MORE ON GREEN FUNCTION TECHNIQUES 10 EQUATIONS OF MOTION AND FURTHER
DEVELOPMENTS 207 10.1 EQUATIONS OF MOTION FOR THE INTERACTING PROPAGATOR
207 10.1.1 EQUATIONS OF MOTION AND GROUND-STATE ENERGY 208 10.2
TIME-DEPENDENT PROBLEMS.: 208 10.2.1 AUGER INDUCED IONIC DESORPTION:
KNOTEK-FEIBELMAN MECHANISM 210 10.3 HIERARCHY OF GREENS FUNCTIONS 212
10.4 COMPOSITE OPERATOR METHOD 213 PROBLEMS 216 11 FEYNMAN DIAGRAMS FOR
CONDENSED MATTER PHYSICS 217 11.1 DIAGRAMS FOR THE VACUUM PROPAGATOR 217
11.1.1 WICK'S THEOREM 219 11.1.2 GOLDSTONE DIAGRAMS 221 11.1.3 DIAGRAM
RULES FOR THE THERMODYNASNIC POTENTIAL 224 11.2 LINKED CLUSTER THEOREM
225 11.2.1 VALENCE ELECTRON AND CORE HOLE 227 11.2.2 H 2 MODEL 229
11.2.3 THE LINKED CLUSTER EXPANSION AND GREEN'S FUNCTIONS . 230 11.3
DIAGRAMS FOR THE DRESSED PROPAGATOR 231 11.3.1 ADIABATIC SWITCHING AND
PERTURBATION THEORY 232 11.3.2 DIAGRAMS FOR THE PROPAGATOR IN FREQUENCY
SPACE 235 11.4 DYSON EQUATION 238 CONTENTS XV 11.4.1 EXTERNAL POTENTIAL
241 11.5 SELF-ENERGY FROM INTERACTIONS 242 11.6 SKELETON DIAGRAMS 245
11.7 TWO-BODY GREEN'S FUNCTION: THE BETHE-SALPETER EQUATION . 245 11.8
SELF-ENERGY AND TWO-BODY GREEN'S FUNCTION 247 11.9 FUNCTIONAL CALCULUS
AND DIAGRAMS 248 11.9.1 THE SELF-ENERGY AS A FUNCTIONAL 249 11.9.2
POLARIZATION BUBBLE : 251 11.9.3 THE VERTEX 253 11.10 HEDIN'S EQUATIONS
254 12 MANY-BODY EFFECTS AND FURTHER THEORY 257 12.1 HIGH DENSITY
ELECTRON GAS 257 12.1.1 MORE PHYSICAL INSIGHT ABOUT THE RPA 259 12.2 LOW
DENSITY ELECTRON GAS: LADDER APPROXIMATION 263 12.3 LADDER
APPROXIMATIONS IN ELECTRON SPECTROSCOPIES 264 12.3.1 XPS AND AUGER
SPECTRA FROM METALS 264 12.3.2 THE U 0 PHENOMENON 267 12.3.3 CORRELATION
IN EARLY TRANSITION METALS 270 12.4 CONSERVING APPROXIMATIONS 272 12.4.1
CONTINUITY EQUATION 272 12.4.2 THE $ FUNCTIONAL 274 12.4.3 GAUGE
TRANSFORMATION 275 12.4.4 GROUND-STATE ENERGY AND GRAND POTENTIAL 276
12.4.5 LUTTINGER-WARD AND ABL VARIATIONAL PRINCIPLES 277 12.5
GENERALIZED WARD IDENTITIES 278 12.6 CONNECTION OF DIAGRAMS TO D F T 279
12.6.1 HIGHLIGHTS ON DENSITY FUNCTIONAL THEORY 279 12.6.2 SHAM -
SCHLUTER EQUATION 282 PROBLEMS 283 13 NON-EQUILIBRIUM THEORY 285 13.1
TIME-DEPENDENT PROBES AND NONLINEAR RESPONSE 285 13.2 KADANOFF-BAYM AND
KELDYSH METHODS ; 286 13.3 COMPLEX-TIME INTEGRALS BY LANGRETH'S
TECHNIQUE 288 13.3.1 FINITE TEMPERATURES 290 13.4 KELDYSH-DYSON EQUATION
ON THE CONTOUR 291 13.5 EVOLUTION ON KELDYSH CONTOUR T 294 13.5.1
CONTOUR EVOLUTION OF BOSONS 298 13.6 SELECTED APPLICATIONS OF THE
KELDYSH FORMALISM 298 13.6.1 ATOM-SURFACE SCATTERING 299 13.6.2 QUANTUM
TRANSPORT 304 PROBLEMS 309 XVI CONTENTS PART IV NON-PERTURBATIVE
APPROACHES AND APPLICATIONS 14 SOME RECURSION TECHNIQUES WITH
APPLICATIONS 313 14.1 LANCZOS-HAYDOCK RECURSION 313 14.1.1 LOCAL GREEN'S
FUNCTION FOR A CHAIN 313 14.1.2 GREEN'S FUNCTION OF ANY SYSTEM^. 315
14.1.3 TERMINATOR 316 14.1.4 MOMENTS 322 14.2 SPIN-DISENTANGLED
DIAGONALIZATION 323 14.3 METHOD OF EXCITATION AMPLITUDES 326 14.4
FEENBERG METHOD 329 14.4.1 SOLVING LINEAR SYSTEMS 332 14.4.2 HOMOGENEOUS
SYSTEMS 333 PROBLEMS' 333 15 ASPECTS OF NONLINEAR OPTICS AND MANY-PHOTON
EFFECTS . 335 15.1 DIFFUSION OF RADIATION IN DIPOLE APPROXIMATION 335
15.1.1 SECOND-ORDER PROCESSES 336 15.2 SUM FREQUENCY AND SECOND-HARMONIC
GENERATION (SHG) . 342 15.3 DIFFUSION OF COHERENT LIGHT 343 15.3.1
EFFECTIVE MODE .' 343 15.3.2 DYNAMICAL STARK EFFECT 346 PROBLEMS '. 351
PART V SELECTED EXACT RESULTS IN MANY-BODY PROBLEMS 16 QUANTUM PHASES !
355 16.0.3 GAUGE TRANSFORMATIONS 355 16.0.4 SPINOR ROTATIONS 356 16.0.5
GALILEAN TRANSFORMATIONS 356 16.1 TOPOLOGIC PHASES 357 16.1.1 PARAMETRIC
HAMILTONIANS AND BERRY PHASE 358 16.1.2 POLARIZATION OF SOLIDS 362 17
PAIRING FROM REPULSIVE INTERACTIONS 17.0.3 W = 0 PAIRING IN CU-0
CLUSTERS 369 17.0.4 PAIRING MECHANISM 373 17.0.5 THE W = 0 THEOREM 373
17.0.6 EXAMPLES 375 17.1 SUPERCONDUCTING FLUX QUANTIZATION AND JOSEPHSON
EFFECT 378 PROBLEMS 381 CONTENTS XVII 18 ALGEBRAIC METHODS 383 18.1 LIEB
THEOREMS ON THE HALF FILLED HUBBARD MODEL 383 18.2 BETHE ANSATZ FOR THE
HEISENBERG CHAIN 387 18.3 BETHE ANSATZ FOR INTERACTING FERMIONS 1
DIMENSION 392 18.3.1 5- FUNCTION INTERACTION 392 18.3.2 THE HUBBARD
MODEL IN ID 396 18.3.3 THE PERIODIC BOUNDARY CONDITIONS 401 18.3.4 SPIN
CHAIN ANALOGY -: 403 PROBLEMS 406 PART VI APPENDICES 19 APPENDIX 1:
ZERO-POINT ENERGY IN A PILLBOX 409 20 APPENDIX II-CHARACTER TABLES 411
21 PROOF OF THE WIGNER-ECKART THEOREM 413 SOLUTIONS 415 REFERENCES 431
INDEX 439 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Cini, Michele 1946- |
| author_GND | (DE-588)129212113 |
| author_facet | Cini, Michele 1946- |
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| author_variant | m c mc |
| building | Verbundindex |
| bvnumber | BV022474414 |
| callnumber-first | Q - Science |
| callnumber-label | QC173 |
| callnumber-raw | QC173.454 |
| callnumber-search | QC173.454 |
| callnumber-sort | QC 3173.454 |
| callnumber-subject | QC - Physics |
| classification_rvk | UP 1300 |
| ctrlnum | (OCoLC)123375609 (DE-599)BVBBV022474414 |
| dewey-full | 530.41 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.41 |
| dewey-search | 530.41 |
| dewey-sort | 3530.41 |
| dewey-tens | 530 - Physics |
| discipline | Physik Geographie |
| discipline_str_mv | Physik Geographie |
| format | Book |
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| id | DE-604.BV022474414 |
| illustrated | Illustrated |
| index_date | 2024-07-02T17:45:53Z |
| indexdate | 2024-07-20T09:18:19Z |
| institution | BVB |
| isbn | 9783540707264 3540707263 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015681846 |
| oclc_num | 123375609 |
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| physical | XVII, 443 S. Ill., graph. Dast. |
| publishDate | 2007 |
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| publisher | Springer |
| record_format | marc |
| spelling | Cini, Michele 1946- Verfasser (DE-588)129212113 aut Topics and methods in condensed matter theory from basic quantum mechanics to the frontiers of research Michele Cini Berlin [u.a.] Springer 2007 XVII, 443 S. Ill., graph. Dast. txt rdacontent n rdamedia nc rdacarrier Matière condensée Condensed matter Kondensierte Materie (DE-588)4132810-3 gnd rswk-swf Theoretische Physik (DE-588)4117202-4 gnd rswk-swf Kondensierte Materie (DE-588)4132810-3 s Theoretische Physik (DE-588)4117202-4 s DE-604 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2905067&prov=M&dok_var=1&dok_ext=htm Inhaltstext HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015681846&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cini, Michele 1946- Topics and methods in condensed matter theory from basic quantum mechanics to the frontiers of research Matière condensée Condensed matter Kondensierte Materie (DE-588)4132810-3 gnd Theoretische Physik (DE-588)4117202-4 gnd |
| subject_GND | (DE-588)4132810-3 (DE-588)4117202-4 |
| title | Topics and methods in condensed matter theory from basic quantum mechanics to the frontiers of research |
| title_auth | Topics and methods in condensed matter theory from basic quantum mechanics to the frontiers of research |
| title_exact_search | Topics and methods in condensed matter theory from basic quantum mechanics to the frontiers of research |
| title_exact_search_txtP | Topics and methods in condensed matter theory from basic quantum mechanics to the frontiers of research |
| title_full | Topics and methods in condensed matter theory from basic quantum mechanics to the frontiers of research Michele Cini |
| title_fullStr | Topics and methods in condensed matter theory from basic quantum mechanics to the frontiers of research Michele Cini |
| title_full_unstemmed | Topics and methods in condensed matter theory from basic quantum mechanics to the frontiers of research Michele Cini |
| title_short | Topics and methods in condensed matter theory |
| title_sort | topics and methods in condensed matter theory from basic quantum mechanics to the frontiers of research |
| title_sub | from basic quantum mechanics to the frontiers of research |
| topic | Matière condensée Condensed matter Kondensierte Materie (DE-588)4132810-3 gnd Theoretische Physik (DE-588)4117202-4 gnd |
| topic_facet | Matière condensée Condensed matter Kondensierte Materie Theoretische Physik |
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