Density matrix theory and applications:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin ; Heidelberg
Springer
2012
|
| Ausgabe: | 3. ed. |
| Schriftenreihe: | Springer series on atomic, optical, and plasma physics
63 |
| Schlagwörter: | |
| Links: | http://deposit.dnb.de/cgi-bin/dokserv?id=3705620&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024780755&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XVIII, 343 S. graph. Darst. |
| ISBN: | 9783642205606 9783642205613 3642205607 |
Internformat
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Datensatz im Suchindex
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|---|---|
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| DE-BY-TUM_location | LSB |
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| adam_text | IMAGE 1
CONTENTS
1 BASIC CONCEPTS 1
1.1 SPIN STATES AND DENSITY MATRIX OF SPIN-1/2 PARTICLES 1
1.1.1 PURE SPIN STATES 1
1.1.2 THE POLARIZATION VECTOR 4
1.1.3 MIXED SPIN STATES 7
1.1.4 PURE VERSUS MIXED STATES 9
1.1.5 THE SPIN-DENSITY MATRIX AND ITS BASIC PROPERTIES 11 1.1.6 THE
ALGEBRA OF THE PAULI MATRICES 17
1.1.7 SUMMARY 20
1.2 POLARIZATION STATES AND DENSITY MATRIX OF PHOTONS 21
1.2.1 THE CLASSICAL CONCEPT OF WAVE POLARIZATION 21
1.2.2 PURE AND MIXED POLARIZATION STATES OF PHOTONS 24 1.2.3 THE QUANTUM
MECHANICAL CONCEPT OF PHOTON SPIN 25 1.2.4 THE POLARIZATION DENSITY
MATRIX 27
1.2.5 STOKES PARAMETER DESCRIPTION 29
2 GENERAL DENSITY MATRIX THEORY 35
2.1 PURE AND MIXED QUANTUM MECHANICAL STATES 35
2.2 THE DENSITY MATRIX AND ITS BASIC PROPERTIES 38
2.3 COHERENCE VERSUS INCOHERENCE 43
2.3.1 ELEMENTARY THEORY OF QUANTUM BEATS 43
2.3.2 THE CONCEPT OF COHERENT SUPERPOSITION 45
2.4 TIME EVOLUTION OF STATISTICAL MIXTURES 47
2.4.1 THE TIME EVOLUTION OPERATOR 47
2.4.2 THE LIOUVILLE EQUATION 50
2.4.3 THE INTERACTION PICTURE 52
2.5 SPIN PRECESSION IN A MAGNETIC FIELD 57
2.6 SYSTEMS IN THERMAL EQUILIBRIUM 58
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1010702734
DIGITALISIERT DURCH
IMAGE 2
XIV CONTENTS
3 COUPLED SYSTEMS 61
3.1 THE NONSEPARABILITY OF QUANTUM SYSTEMS AFTER AN INTERACTION 61 3.2
INTERACTION WITH AN UNOBSERVED SYSTEM. THE REDUCED DENSITY MATRIX 63
3.3 ANALYSIS OF LIGHT EMITTED BY ATOMS (NUCLEI) 67
3.3.1 THE COHERENCE PROPERTIES OF THE POLARIZATION STATES 67 3.3.2
DESCRIPTION OF THE EMITTED PHOTON 69
3.4 SOME FURTHER CONSEQUENCES OF THE PRINCIPLE OF NONSEPARABILITY.... 71
3.4.1 COLLISIONAL SPIN DEPOLARIZATION 71
3.4.2 COMPLETE COHERENCE IN ATOMIC EXCITATION 72
3.5 EXCITATION OF ATOMS BY ELECTRON IMPACT 1 74
3.5.1 THE REDUCED DENSITY MATRIX OF THE ATOMIC SYSTEM 74 3.5.2
RESTRICTIONS DUE TO SYMMETRY REQUIREMENTS 78
3.6 NONSEPARABILITY, ENTANGLEMENT, AND CORRELATIONS IN TWO-PARTICLE
SPIN-1/2 SYSTEMS 82
3.6.1 INTRODUCTION AND BASIC DEFINITIONS 82
3.6.2 TWO-PARTICLE DENSITY MATRICES AND REDUCED DENSITY MATRICES.
CRITERION FOR ENTANGLEMENT 84 3.6.3 CORRELATION PARAMETERS AND THEIR
INTERPRETATION. JOINT PROBABILITIES 87
3.6.4 ENTANGLEMENT VERSUS CLASSICAL CORRELATIONS. LOCC-PROCEDURES.
ENTANGLEMENT IN MIXTURES 92 3.6.5 STATES WITH MAXIMAL ENTANGLEMENT.
ENTROPY OF ENTANGLEMENT. BELL STATES 97
3.6.6 CORRELATIONS IN THE SINGLET STATES. CONDITIONAL PROBABILITIES 104
3.6.7 ENTANGLEMENT AND NON-LOCALITY. BELL INEQUALITIES 109 3.6.8
EXPERIMENTAL TESTS. CONCLUSIONS 112
4 IRREDUCIBLE COMPONENTS OF THE DENSITY MATRIX 115
4.1 INTRODUCTION 115
4.2 THE DEFINITION OF TENSOR OPERATORS 116
4.2.1 THE GENERAL CONSTRUCTION RULE 116
4.2.2 TRANSFORMATION PROPERTIES UNDER ROTATIONS. THE ROTATION MATRIX 118
4.2.3 EXAMPLES 121
4.2.4 SOME IMPORTANT PROPERTIES OF THE TENSOR OPERATORS 122 4.3 STATE
MULTIPOLES (STATISTICAL TENSORS) 124
4.3.1 DEFINITION OF STATE MULTIPOLES 124
4.3.2 BASIC PROPERTIES OF STATE MULTIPOLES 126
4.3.3 PHYSICAL INTERPRETATION OF STATE MULTIPOLES. THE ORIENTATION
VECTOR AND ALIGNMENT TENSOR 127 4.4 EXAMPLES: SPIN TENSORS 129
4.4.1 SPIN TENSORS FOR SPIN-1/2 PARTICLES 129
4.4.2 DESCRIPTION OF SPIN-1 PARTICLES 130
IMAGE 3
CONTENTS
4.5 SYMMETRY PROPERTIES. RELATION BETWEEN SYMMETRY AND COHERENCE 134
4.5.1 AXIALLY SYMMETRIC SYSTEMS 134
4.5.2 CLASSIFICATION OF AXIALLY SYMMETRIC SYSTEMS 135 4.5.3 EXAMPLES:
PHOTOABSORPTION BY ATOMS (NUCLEI) 139 4.6 EXCITATION OF ATOMS BY
ELECTRON IMPACT II: STATE MULTIPOLES 140 4.6.1 COLLISONAL PRODUCTION OF
ATOMIC ORIENTATION 140
4.6.2 GENERAL CONSEQUENCES OF REFLECTION INVARIANCE 142 4.6.3 AXIALLY
SYMMETRIC ATOMIC SYSTEMS 144
4.6.4 SYMMETRY RELATIONS IN THE NATURAL SYSTEM 145 4.6.5 COORDINATE
REPRESENTATION OF THE DENSITY MATRIX. SHAPE AND SPATIAL ORIENTATION OF
ATOMIC CHARGE CLOUDS ... 147 4.7 TIME EVOLUTION OF STATE MULTIPOLES IN
THE PRESENCE OF AN EXTERNAL PERTURBATION 153
4.7.1 THE PERTURBATION COEFFICIENTS 153
4.7.2 PERTURBATION COEFFICIENTS FOR THE FINE AND HYPERFINE INTERACTIONS
155
4.7.3 AN EXPLICIT EXAMPLE 160
4.7.4 INFLUENCE OF AN EXTERNAL MAGNETIC FIELD 161
4.8 NOTATIONS USED BY OTHER AUTHORS 162
RADIATION FROM POLARIZED ATOMS. QUANTUM BEATS 165
5.1 GENERAL THEORY I: DENSITY MATRIX DESCRIPTION OF RADIATIVE DECAY
PROCESSES 165
5.2 GENERAL THEORY II: SEPARATION OF DYNAMICAL AND GEOMETRICAL FACTORS
169
5.3 DISCUSSION OF THE GENERAL FORMULAS 171
5.3.1 GENERAL STRUCTURE OF THE EQUATIONS 171
5.3.2 MANIFESTATIONS OF COHERENCE. QUANTUM BEATS 173 5.4 PERTURBED
ANGULAR DISTRIBUTION AND POLARIZATION 175
5.4.1 GENERAL THEORY 175
5.4.2 QUANTUM BEATS PRODUCED BY SYMMETRY BREAKING 176 5.5 TIME
INTEGRATION OVER QUANTUM BEATS 178
5.5.1 STEADY-STATE EXCITATION 178
5.5.2 DEPOLARIZATION EFFECTS CAUSED BY FINE AND HYPERFINE INTERACTIONS
179
SOME APPLICATIONS 183
6.1 THEORY OF ELECTRON-PHOTON ANGULAR CORRELATIONS IN ATOMIC PHYSICS 183
6.1.1 SINGLET-SINGLET TRANSITIONS 183
6.1.2 INFLUENCE OF FINE AND HYPERFINE INTERACTIONS ON THE EMITTED
RADIATION 188
6.2 STEADY-STATE EXCITATION 189
6.2.1 POLARIZATION OF IMPACT RADIATION 189
6.2.2 THRESHOLD AND PSEUDOTHRESHOLD EXCITATIONS 191
IMAGE 4
CONTENTS
6.3 EFFECT OF A WEAK MAGNETIC FIELD 193
6.3.1 PERTURBATION COEFFICIENTS FOR VARIOUS GEOMETRIES COHERENCE
PHENOMENA 193
6.3.2 MAGNETIC DEPOLARIZATION. THEORY OF THE HANLE EFFECT 197 6.3.3
PHYSICAL INTERPRETATION OF ZEEMAN QUANTUM BEATS. ROTATION OF THE ATOMIC
CHARGE CLOUD 200
6.4 INFLUENCE OF ELECTRIC FIELDS. ORIENTATION - ALIGNMENT CONVERSION...
203 6.4.1 TIME EVOLUTION OF STATE MULTIPOLES 203
6.4.2 VARIATION OF SHAPE AND SPATIAL DIRECTION OF ATOMIC CHARGE CLOUDS
205
6.4.3 CREATION OF ORIENTATION OUT OF ALIGNMENT 208
6.4.4 COMPARISON BETWEEN ELECTRIC AND MAGNETIC FIELD INFLUENCES 208
THE ROLE OF ORIENTATION AND ALIGNMENT IN MOLECULAR PROCESSES 209 7.1
INTRODUCTION 209
7.2 ROTATIONAL POLARIZATION. SEMICLASSICAL INTERPRETATION OF STATE
MULTIPOLES: DISTRIBUTION FUNCTIONS OF ANGULAR MOMENTUM VECTORS 210
7.3 AXIS DISTRIBUTIONS OF LINEAR ROTORS 214
7.3.1 BASIC RELATIONS. STATES WITH SHARP J AND M 214
7.3.2 GENERAL EQUATIONS. EXAMPLES AND EXPERIMENTAL STUDIES 216 7.4 ORDER
PARAMETERS: GENERAL DESCRIPTION OF AXIS ORIENTATION AND ALIGNMENT 219
7.4.1 GENERAL THEORY FOR LINEAR MOLECULES AND EXAMPLES 219
7.4.2 RELATION BETWEEN ANGULAR MOMENTA AND AXIS DISTRIBUTIONS FOR LINEAR
ROTORS. PENDULUM STATES 223 7.5 ANGULAR MOMENTA AND AXIS DISTRIBUTIONS
OF ROTORS AFTER PHOTOABSORPTION. QUANTUM MECHANICAL
AND CLASSICAL THEORY 224
7.5.1 ABSORPTION OF LINEARLY POLARIZED LIGHT 224
7.5.2 ABSORPTION OF CIRCULARLY POLARIZED AND UNPOLARIZED LIGHT 227
7.6 DISTRIBUTION FUNCTIONS FOR NONLINEAR MOLECULES AND FOR DIATOMICS
WITH ELECTRONIC ANGULAR MOMENTUM 230 7.6.1 MOLECULAR ORIENTATION EULER
ANGLES 230
7.6.2 ANGULAR MOMENTUM AND AXIS DISTRIBUTIONS OF SYMMETRIC TOPS 231
7.6.3 THEORY OF ORIENTED SYMMETRIC-TOP MOLECULES. SEMICLASSICAL
INTERPRETATION 233
7.6.4 ORDER PARAMETERS FOR NONLINEAR MOLECULES 235
IMAGE 5
CONTENTS XVII
7.7 ELECTRONIC ORBITAL ORIENTATION AND ALIGNMENT 237
7.7.1 BASIC CONCEPTS. SPACE-FIXED MOLECULES: EXCITED STATE COHERENCE 237
7.7.2 ROTATING MOLECULES. STATES WITH DEFINITE PARITY: SPATIAL
ORIENTATION AND SELECTIVE POPULATION 241 7.7.3 COMBINED DESCRIPTION OF
ROTATIONAL POLARIZATION AND ORBITAL ANISOTROPIES 245
7.7.4 VECTOR CORRELATIONS. ANALYSIS OF EMITTED LIGHT 249 7.7.5
PHOTOABSORPTION AND PHOTOFRAGMENTATION 253
7.8 DYNAMICAL STEREOCHEMISTRY 256
7.8.1 GENERAL EXPRESSIONS AND DEFINITION OF STERIC FACTORS 256 7.8.2
DISCUSSION AND EXAMPLES 263
7.8.3 PRODUCT ROTATIONAL POLARIZATION. QUANTUM MECHANICAL THEORY AND
SEMICLASSICAL APPROXIMATION 267 7.8.4 ALIGNMENT-INDUCED CHEMICAL
REACTIONS 271
8 QUANTUM THEORY OF RELAXATION 275
8.1 DENSITY MATRIX EQUATIONS FOR DISSIPATIVE QUANTUM SYSTEMS 275
8.1.1 CONDITIONS OF IRREVERSIBILITY. MARKOFF PROCESSES 275 8.1.2 TIME
CORRELATION FUNCTIONS. DISCUSSION OF THE MARKOFF APPROXIMATION 278
8.1.3 THE RELAXATION EQUATION. THE SECULAR APPROXIMATION 280 8.2 RATE
(MASTER) EQUATIONS 284
8.3 KINETICS OF STIMULATED EMISSION AND ABSORPTION 288
8.4 THE BLOCH EQUATIONS 294
8.4.1 MAGNETIC RESONANCE 294
8.4.2 LONGITUDINAL AND TRANSVERSE RELAXATION. SPIN ECHOES 298 8.4.3 THE
OPTICAL BLOCH EQUATIONS 301
8.5 SOME PROPERTIES OF THE RELAXATION MATRIX 302
8.5.1 GENERAL CONSTRAINTS 302
8.5.2 RELAXATION OF STATE MULTIPOLES 304
8.6 THE LIOUVILLE FORMALISM 306
8.7 LINEAR RESPONSE OF A QUANTUM SYSTEM TO AN EXTERNAL PERTURBATION 310
APPENDIXES 313
A.I APPENDIX A: THE DIRECT PRODUCT 313
B. 1 APPENDIX B: STATE MULTIPOLES FOR COUPLED SYSTEMS 316 C.I APPENDIX
C: FORMULAS FROM ANGULAR MOMENTUM THEORY 318 C. 1.1 ROTATION MATRIX
ELEMENTS 320
C.I.2 MATRIX ELEMENTS OF IRREDUCIBLE TENSOR OPERATORS 321 C.1.3
SPHERICAL HARMONICS 321
D. 1 APPENDIX D: THE EFFICIENCY OF A MEASURING DEVICE 321 E. 1 APPENDIX
E: THE SCATTERING AND TRANSITION OPERATORS 323
IMAGE 6
XVUEI CONTENTS
F. 1 APPENDIX F: SOME CONSEQUENCES OF DENSITY MATRIX THEORY FOR
POLARIZATION VECTORS AND TENSORS 324
G. 1 APPENDIX G: DERIVATION OF EQUATION (3.66B) 328
H. 1 APPENDIX H: CONDITIONS FOR MAXIMAL ENTANGLEMENT 329 1.1 APPENDIX I:
PROPERTIES OF MAXIMALLY ENTANGLED STATES 330 J.I APPENDIX J: EIGENVALUES
OF DENSITY MATRICES CONDITION FOR SEPARABILITY SCHMIDT-DECOMPOSITION 333
REFERENCES 337
INDEX 341
|
| any_adam_object | 1 |
| author | Blum, Karl 1937- |
| author_GND | (DE-588)136353290 |
| author_facet | Blum, Karl 1937- |
| author_role | aut |
| author_sort | Blum, Karl 1937- |
| author_variant | k b kb |
| building | Verbundindex |
| bvnumber | BV039922293 |
| classification_rvk | UK 1000 UK 1200 |
| classification_tum | PHY 500f PHY 026f |
| ctrlnum | (OCoLC)725042395 (DE-599)DNB1010702734 |
| dewey-full | 530.133 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.133 |
| dewey-search | 530.133 |
| dewey-sort | 3530.133 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| edition | 3. ed. |
| format | Book |
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| id | DE-604.BV039922293 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T16:05:22Z |
| institution | BVB |
| isbn | 9783642205606 9783642205613 3642205607 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024780755 |
| oclc_num | 725042395 |
| open_access_boolean | |
| owner | DE-703 DE-20 DE-19 DE-BY-UBM DE-91G DE-BY-TUM |
| owner_facet | DE-703 DE-20 DE-19 DE-BY-UBM DE-91G DE-BY-TUM |
| physical | XVIII, 343 S. graph. Darst. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Springer |
| record_format | marc |
| series | Springer series on atomic, optical, and plasma physics |
| series2 | Springer series on atomic, optical, and plasma physics |
| spellingShingle | Blum, Karl 1937- Density matrix theory and applications Springer series on atomic, optical, and plasma physics Atomphysik (DE-588)4003423-9 gnd Dichtematrix (DE-588)4149624-3 gnd |
| subject_GND | (DE-588)4003423-9 (DE-588)4149624-3 |
| title | Density matrix theory and applications |
| title_auth | Density matrix theory and applications |
| title_exact_search | Density matrix theory and applications |
| title_full | Density matrix theory and applications Karl Blum |
| title_fullStr | Density matrix theory and applications Karl Blum |
| title_full_unstemmed | Density matrix theory and applications Karl Blum |
| title_short | Density matrix theory and applications |
| title_sort | density matrix theory and applications |
| topic | Atomphysik (DE-588)4003423-9 gnd Dichtematrix (DE-588)4149624-3 gnd |
| topic_facet | Atomphysik Dichtematrix |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3705620&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024780755&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV013270105 |
| work_keys_str_mv | AT blumkarl densitymatrixtheoryandapplications |
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