Simple models of many-fermion systems:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2010
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben. - Zusätzliches Online-Angebot unter http://extra.springer.com. |
| Physical Description: | XI, 279 S. graph. Darst. 24 cm |
| ISBN: | 9783642038389 |
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MARC
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| 245 | 1 | 0 | |a Simple models of many-fermion systems |c Joachim Alexander Maruhn ; Paul-Gerhard Reinhard ; Eric Suraud |
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Record in the Search Index
| _version_ | 1804143360541196288 |
|---|---|
| adam_text | IN FINITE SYSTEMS 55 CONTENTS 1.1.1 .2 .3 .4 .5 .6 .7 1 THE VARIETY OF
FINITE FERMION SYSTEMS AND THEIR BASIC PROPERTIES 1 1 .1 FERMIONS IN THE
UNIVERSE 3 THE FOUR ELEMENTARY INTERACTIONS 3 BASICS OF NUCLEI 4 BASICS
OF THE ELECTRONIC CLOUD IN ATOMS 8 BASICS OF MOLECULAR BINDING 12 BASICS
OF METAL CLUSTERS 14 QUANTUM DOTS 19 BASICS OF 3 HE DROPLETS 21 .8
DEGENERATE FERMION GAS: ATOM TRAPS, WHITE DWARFS, NEUTRON STARS 22 1.2
SIMILAR AND DIFFERENT 26 1.2.1 OVERVIEW OF MANY-FERMION SYSTEMS 26 1.2.2
SCALES AND INTERACTIONS 27 1.2.3 SHELLS IN FINITE SYSTEMS 29 1.2.4
BEYOND THE STATIC MEAN FIELD 31 1.3 BASIC THEORETICAL TOOLS 35 1.3.1 THE
WAVE FUNCTION APPROACH 35 1.3.2 CREATION AND ANNIHILATION OPERATORS 37
1.3.3 DENSITY MATRICES 40 1.4 CONCLUDING REMARKS 42 2 THE FERMI-GAS
MODEL 45 2.1 FROM FINITE BOX TO CONTINUUM STATES 46 2.1.1 SINGLE-FERMION
WAVE FUNCTIONS IN GENERAL 46 2.1.2 FROM BOUND STATES TO PLANE WAVES 47
2.2 BASICS: DENSITY, FERMI MOMENTUM, FERMI ENERGY 51 2.2.1 FERMI
MOMENTUM, FERMI ENERGY, DENSITY 51 2.2.2 THE ONE-BODY DENSITY MATRIX 53
2.2.3 A MODEL FOR THE ONE-BODY DENSITY MATRIX BIBLIOGRAFISCHE
INFORMATIONEN HTTP://D-NB.INFO/995947015 DIGITALISIERT DURCH I CONTENTS
2.2.4 THE TWO-BODY DENSITY 56 2.2.5 THE KINETIC ENERGY 57 2.2.6 THE
LEVEL DENSITY 59 2.3 FERMI GAS AT FINITE TEMPERATURE 59 2.4 FERMI GAS IN
STARS: THE EXAMPLE OF WHITE DWARFS 63 2.4.1 LOW DENSITIES 63 2.4.2
STABILITY IN THE RELATIVISTIC DOMAIN 64 2.5 COULOMB ENERGY OF A CHARGED
FERMI GAS 66 2.6 CONCLUDING REMARKS 69 3 PARTICLES IN AN EXTERNAL FIELD
71 3.1 THE VARIETY OF SHELL-MODEL POTENTIALS 71 3.1.1 SATURATING FERMION
SYSTEMS 71 3.1.2 ATOMIC SYSTEMS 73 3.2 THE HARMONIC OSCILLATOR IN THE
VARIOUS SUBFIELDS 74 3.2.1 THE HARMONIC OSCILLATOR IN TWO AND THREE
DIMENSIONS 75 3.2.2 THE 3D OSCILLATOR ATOMIC TRAPS 76 3.2.3 THE 2D
OSCILLATOR FOR QUANTUM DOTS 76 3.2.4 THE CLEMENGER-NILSSON MODEL FOR
METAL CLUSTERS 77 3.2.5 THE NILSSON MODEL FOR NUCLEI 78 3.2.6 COMPARISON
OF SPECTRA 79 3.3 APPLICATIONS 80 3.3.1 METAL CLUSTERS 80 3.3.2 QUANTUM
DOT IN A MAGNETIC FIELD 83 3.3.3 NUCLEI 85 3.4 CONCLUDING REMARKS 91 4
APPROACHES BASED ON MODEL SPACES 93 4.1 VALENCE-BOND THEORY 94 4.1.1
DIMER MOLECULES 94 4.1.2 A- AND ^-ORBITALS 95 4.1.3 POLYATOMIC MOLECULES
97 4.2 LINEAR COMBINATION OF ATOMIC ORBITALS (LCAO) 99 4.2.1 LCAO IN
DIMER MOLECULES 100 4.2.2 A QUICK LOOK AT NEUTRAL DIMERS 104 4.2.3 FROM
DIMER TO LARGE MOLECULES 105 4. CONTENTS IX 5 HARTREE-FOCK 117 5.1 THE
HARTREE-FOCK SETUP 117 5.1.1 FOUNDATION 117 5.1.2 THE HARTREE-FOCK
APPROXIMATION 118 5.1.3 THE SPACE OF VARIATIONS OF A SLATER STATE 120
5.2 THE HARTREE-FOCK EQUATIONS 121 5.2.1 IN TERMS OF FERMION OPERATORS
121 5.2.2 IN CONFIGURATION SPACE (MATRIX ELEMENTS) 122 5.2.3 IN
COORDINATE SPACE 124 5.3 THE HARTREE-FOCK ENERGY 126 5.3.1 THE TOTAL
ENERGY 126 5.3.2 THE INTERPRETATION OF SINGLE-PARTICLE ENERGIES:
KOOPMAN S THEOREM 127 5.3.3 EXCITATIONS AND EXCITATION ENERGIES 128 5.4
THE DENSITY MATRIX FORMULATION 129 5.5 A SIMPLE TEST CASE: TWO PARTICLES
IN ID 130 5.5.1 THE MODEL 130 5.5.2 THE TOTAL ENERGY 131 5.5.3 THE
HARTREE-FOCK EQUATION 132 5.5.4 A CLOSED SOLUTION 133 5.5.5 SYMMETRY
BREAKING 134 5.6 AN ILLUSTRATIVE EXAMPLE: THE HE ATOM 135 5.6.1
HAMILTONIAN AND HF EQUATIONS 136 5.6.2 VARIATIONAL ANSATZ 137 5.6.3 FULL
HF SOLUTION 139 5.7 CONCLUDING REMARKS 140 6 DENSITY FUNCTIONAL THEORY
143 6.1 BASICS OF ELECTRONIC DENSITY FUNCTIONAL THEORY (DFT) 144 6.1.1
THE HOHENBERG-KOHN THEOREM 144 6.1.2 THE LOCAL DENSITY APPROXIMATION 145
6.1.3 KOHN-SHAM APPROACH 147 6.2 BACK TO THE EXAMPLE OF THE HE ATOM 149
6.3 SELF-INTERACTION CORRECTION (SIC) 151 6.4 THE SKYRME ENERGY
FUNCTIONAL IN NUCLEAR PHYSICS 153 6. X CONTENTS 7.2 THE QUASISPIN
ALGEBRA 167 7.3 THE UNPERTURBED GROUND STATE 168 7.4 THE ELEMENTARY
EXCITATIONS 169 7.5 EXACT SOLUTION 170 7.6 HARTREE-FOCK SOLUTION 171
7.6.1 THE SPACE OF SLATER STATES IN THE LMG 171 7.6.2 EXPECTATION VALUES
WITH THE TRANSFORMED STATE 173 7.6.3 THE ENERGY LANDSCAPE AND THE HF
MINIMUM 175 7.7 SPONTANEOUS SYMMETRY BREAKING 178 7.7.1 VIOLATION OF
REFLECTION SYMMETRY IN THE LMG MODEL 178 7.7.2 TRANSITION FROM
SPHERICAL TO DEFORMED NUCLEI 180 7.7.3 THE JAHN-TELLER EFFECT 181 7.7.4
SYMMETRY RESTORATION BY PROJECTION 183 7.8 CONCLUDING REMARKS 185 8
EXCITATION SPECTRA 187 8. 1 COLLECTIVE EFFECTS IN EXCITATION SPECTRA 188
8.2 THE TIME-DEPENDENT HARTREE-FOCK APPROXIMATION 190 8.2.1 INTUITIVE
FORMULATION 190 8.2.2 TIME-DEPENDENT VARIATIONAL PRINCIPLE 191 8.2.3
TDHF BEYOND THE LINEAR DOMAIN 192 8.3 RPA - THE ALGEBRA OF
SMALL-AMPLITUDE OSCILLATIONS 192 8.3.1 THE STARTING POINT: TDHF 193
8.3.2 LINEARIZATION 194 8.3.3 EIGENMODES AND EIGENFREQUENCIES 195 8.3.4
THE RPA EQUATIONS IN MATRIX FORM 197 8.3.5 TRANSITION MOMENTS AND
STRENGTH DISTRIBUTIONS 199 8.3.6 RPA EQUATIONS IN CONNECTION WITH DFT
200 8.3.7 RPA IN THE LMG MODEL AS EXAMPLE 202 8.3.8 A PRACTICAL EXAMPLE:
GDR IN THE NUCLEUS 238 (/ 205 8.4 SUM RULES AND SUM-RULE APPROXIMATIONS
206 8.4. CONTENTS X 9.3.2 A SCHEMATIC DESCRIPTION OF THE PAIRING
INTERACTION 225 9.3.3 SENIORITY MODEL AND QUASISPIN ALGEBRA 226 9.3.4
ODD N AND ODD-EVEN STAGGERING 229 9.4 PAIRING AND THE BCS MODEL 231
9.4.1 THE BCS STATE 231 9.4.2 THE GAP EQUATION 234 9.4.3 BCS FOR
CONTINUOUS SPECTRA 236 9.5 CONCLUDING REMARKS 238 10 CONCLUSIONS 24 1 A
QUANTUM-MECHANICAL BACKGROUND 243 A. 1 SPHERICAL SINGLE-PARTICLE WAVE
FUNCTIONS 243 A. 1.1 GENERAL FORM 243 A.1.2 HARMONIC OSCILLATOR 244
A.1.3 THE HYDROGEN ATOM 246 A.1.4 THE SPHERICAL SQUARE WELL (BOX) 246
A.2 ANGULAR MOMENTUM 247 A.2.1 ANGULAR MOMENTUM ALGEBRA 247 A.2.2
ANGULAR MOMENTUM COUPLING 249 A.2.3 COUPLED AND UNCOUPLED BASIS 250
A.2.4 SPIN COUPLING 251 A.2.5 MATRIX ELEMENT OF L S 251 A.3
INDEPENDENT-PARTICLE WAVE FUNCTIONS 252 A.4 ALGEBRA OF FERMION OPERATORS
253 A.4.1 FOCK SPACE 253 A.4.2 OPERATORS IN FOCK SPACE 255 A.4.3 FIELD
OPERATORS 259 A.5 HIERARCHY OF DENSITY OPERATORS 259 A.5.1 THE ONE-BODY
DENSITY 259 A.5.2 THE ONE-BODY DENSITY MATRIX 261 A.5.3 THE TWO-BODY
DENSITY 263 A.6 TIME REVERSAL AND KRAMERS DEGENERACY 263 B USEFUL TABLES
267 B.I UNITS 267 B.2 HERMITE AND LAGUERRE POLYNOMIALS 269 B.2.
|
| any_adam_object | 1 |
| author | Maruhn, Joachim 1949- Reinhard, Paul-Gerhard 1945- Suraud, Eric 1959- |
| author_GND | (DE-588)131641026 (DE-588)128782633 (DE-588)128782641 |
| author_facet | Maruhn, Joachim 1949- Reinhard, Paul-Gerhard 1945- Suraud, Eric 1959- |
| author_role | aut aut aut |
| author_sort | Maruhn, Joachim 1949- |
| author_variant | j m jm p g r pgr e s es |
| building | Verbundindex |
| bvnumber | BV036714739 |
| ctrlnum | (OCoLC)646139027 (DE-599)DNB995947015 |
| dewey-full | 530.12 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.12 |
| dewey-search | 530.12 |
| dewey-sort | 3530.12 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Book |
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| id | DE-604.BV036714739 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:46:26Z |
| institution | BVB |
| isbn | 9783642038389 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020632745 |
| oclc_num | 646139027 |
| open_access_boolean | |
| owner | DE-29T |
| owner_facet | DE-29T |
| physical | XI, 279 S. graph. Darst. 24 cm |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer |
| record_format | marc |
| spelling | Maruhn, Joachim 1949- Verfasser (DE-588)131641026 aut Simple models of many-fermion systems Joachim Alexander Maruhn ; Paul-Gerhard Reinhard ; Eric Suraud Berlin [u.a.] Springer 2010 XI, 279 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Literaturangaben. - Zusätzliches Online-Angebot unter http://extra.springer.com. Fermionensystem (DE-588)4252865-3 gnd rswk-swf Fermionensystem (DE-588)4252865-3 s DE-604 Reinhard, Paul-Gerhard 1945- Verfasser (DE-588)128782633 aut Suraud, Eric 1959- Verfasser (DE-588)128782641 aut DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020632745&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Maruhn, Joachim 1949- Reinhard, Paul-Gerhard 1945- Suraud, Eric 1959- Simple models of many-fermion systems Fermionensystem (DE-588)4252865-3 gnd |
| subject_GND | (DE-588)4252865-3 |
| title | Simple models of many-fermion systems |
| title_auth | Simple models of many-fermion systems |
| title_exact_search | Simple models of many-fermion systems |
| title_full | Simple models of many-fermion systems Joachim Alexander Maruhn ; Paul-Gerhard Reinhard ; Eric Suraud |
| title_fullStr | Simple models of many-fermion systems Joachim Alexander Maruhn ; Paul-Gerhard Reinhard ; Eric Suraud |
| title_full_unstemmed | Simple models of many-fermion systems Joachim Alexander Maruhn ; Paul-Gerhard Reinhard ; Eric Suraud |
| title_short | Simple models of many-fermion systems |
| title_sort | simple models of many fermion systems |
| topic | Fermionensystem (DE-588)4252865-3 gnd |
| topic_facet | Fermionensystem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020632745&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT maruhnjoachim simplemodelsofmanyfermionsystems AT reinhardpaulgerhard simplemodelsofmanyfermionsystems AT surauderic simplemodelsofmanyfermionsystems |