Kinetic theory: classical, quantum, and relativistic descriptions
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2003
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| Ausgabe: | 3. ed. |
| Schriftenreihe: | Graduate texts in contemporary physics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 558 - 562 |
| Beschreibung: | XX, 571 S. graph. Darst. : 24 cm |
| ISBN: | 0387955518 9780387955513 |
Internformat
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| 100 | 1 | |a Liboff, Richard L. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Kinetic theory |b classical, quantum, and relativistic descriptions |c Richard L. Liboff |
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| 500 | |a Literaturverz. S. 558 - 562 | ||
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Datensatz im Suchindex
| _version_ | 1804130339917922304 |
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| adam_text | RICHARD L. LIBOFF KINETIC THEORY CLASSICAL, QUANTUM, AND RELATIVISTIC
DESCRIPTIONS THIRD EDITION WITH 112 ILLUSTRATIONS SPRINGER CONTENTS
PREFACE TO THE THIRD EDITION IX 1 THE LIOUVILLE EQUATION 1 1.1 ELEMENTS
OF CLASSICAL MECHANICS 2 1.1.1 GENERALIZED COORDINATES AND THE
LAGRANGIAN . . . 2 1.1.2 HAMILTON S EQUATIONS 4 1.1.3 CONSTANTS OF THE
MOTION 6 1.1.4 T-SPACE 7 1.1.5 DYNAMIC REVERSIBILITY 9 1.1.6 EQUATION OF
MOTION FOR DYNAMICAL VARIABLES . . . 10 1.2 CANONICAL TRANSFORMATIONS 11
1.2.1 GENERATING FUNCTIONS 11 1.2.2 GENERATING OTHER TRANSFORMATIONS 14
1.2.3 CANONICAL INVARIANTS 15 1.2.4 GROUP PROPERTY OF CANONICAL
TRANSFORMATIONS . . 15 1.2.5 CONSTANTS OF MOTION AND SYMMETRY 16 1.3
LIOUVILLE THEOREM 3 17 1.3.1 PROOF 17 1.3.2 GEOMETRIC SIGNIFICANCE 18
1.3.3 ACTION GENERATES THE MOTION 19 1.4 LIOUVILLE EQUATION 20 1.4.1 THE
ENSEMBLE: DENSITY IN PHASE SPACE 20 1.4.2 FIRST INTERPRETATION OF
D(Q,P,T) 20 1.4.3 MOST GENERAL SOLUTION: SECOND INTERPRETATION OF
D(Q,P,T) 22 1.4.4 INCOMPRESSIBLE ENSEMBLE 23 1.4.5 METHOD OF
CHARACTERISTICS 24 XIV CONTENTS 1.4.6 SOLUTIONS TO THE INITIAL-VALUE
PROBLEM 25 1.4.7 LIOUVILLE OPERATOR 27 1.5 EIGENFUNCTION EXPANSIONS AND
THE RESOLVENT . 29 1.5.1 LIOUVILLE EQUATION INTEGRATING FACTOR 29 1.5.2
EXAMPLE: THE IDEAL GAS 30 1.5.3 FREE-PARTICLE PROPAGATOR 32 1.5.4 THE
RESOLVENT 33 1.6 DISTRIBUTION FUNCTIONS 35 1.6.1 THIRD INTERPRETATION OF
D(Q,P,T) 35 1.6.2 JOINT-PROBABILITY DISTRIBUTION 36 1.6.3 REDUCED
DISTRIBUTIONS 37 1.6.4 CONDITIONAL DISTRIBUTION 37 1.6.5 S-TUPLE
DISTRIBUTION 38 1.6.6 SYMMETRIC PROPERTIES OF DISTRIBUTIONS 39 1.7
MARKOV PROCESS 41 1.7.1 TWO-TIME DISTRIBUTIONS 41 1.7.2
CHAPMAN-KOLMOGOROV EQUATION 41 1.7.3 HOMOGENEOUS PROCESSES IN TIME 43
1.7.4 MASTER EQUATION 43 1.7.5 APPLICATION TO RANDOM WALK 44 1.8
CENTRAL-LIMIT THEOREM 47 1.8.1 RANDOM VARIABLES AND THE CHARACTERISTIC
FUNCTION 47 1.8.2 EXPECTATION, VARIANCE, AND THE CHARACTERISTIC FUNCTION
1.8.3 SUMS OF RANDOM VARIABLES 1.8.4 APPLICATION TO RANDOM WALK 1.8.5
LARGE N LIMIT: CENTRAL-LIMIT THEOREM 1.8.6 RANDOM WALK IN LARGE N LIMIT
1.8.7 POISSON AND GAUSSIAN DISTRIBUTIONS 1.8.8 COVARIANCE AND
AUTOCORRELATION FUNCTION . . . . PROBLEMS ? 2 ANALYSES OF THE LIOUVILLE
EQUATION 2.1 BBKGY HIERARCHY 2.1.1 LIOUVILLE, KINETIC ENERGY, AND
REMAINDER OPERATORS 2.1.2 REDUCTION OF THE LIOUVILLE EQUATION 2.1.3
FURTHER SYMMETRY REDUCTIONS 2.1.4 CONSERVATION OF ENERGY FROM BYI AND BY
2 . . . 2.2 CORRELATION EXPANSIONS: THE VLASOV LIMIT 2.2.1
NONDIMENSIONALIZATION 2.2.2 CORRELATION FUNCTIONS 2.2.3 THE VLASOV LIMIT
2.2.4 THE VLASOV EQUATION: SELF-CONSISTENT SOLUTION . 2.2.5 DEBYE
DISTANCE AND THE VLASOV LIMIT CONTENTS XV 2.2.6 RADIAL DISTRIBUTION
FUNCTION 96 2.3 DIAGRAMS: PRIGOGINE ANALYSIS 97 2.3.1 PERTURBATION
LIOUVILLE OPERATOR 98 2.3.2 GENERALIZED FOURIER SERIES 99 2.3.3
INTERPRETATION OF A; COEFFICIENTS 99 2.3.4 EQUATIONS OF MOTION FOR A (
K) COEFFICIENTS 102 2.3.5 SELECTION RULES FOR MATRIX ELEMENTS 103 2.3.6
PROPERTIES OF DIAGRAMS 104 2.3.7 LONG-TIME DIAGRAMS: THE BOLTZMANN
EQUATION . 107 2.3.8 REDUCTION OF TIME INTEGRALS 108 2.3.9 APPLICATION
OF DIAGRAMS TO PLASMAS 113 2.4 BOGOLIUBOV HYPOTHESIS 115 2.4.1 TIME AND
LENGTH INTERVALS 115 2.4.2 THE THREE TEMPORAL STAGES 115 2.4.3
BOGOLIUBOV DISTRIBUTIONS 117 2.4.4 DENSITY EXPANSION 117 2.4.5
CONSTRUCTION OF F 2(0) 119 2.4.6 DERIVATION OF THE BOLTZMANN EQUATION
121 2.5 KLIMONTOVICH PICTURE 124 2.5.1 PHASE DENSITIES 124 2.5.2 PHASE
DENSITY AVERAGES 125 2.5.3 RELATION TO CORRELATION FUNCTIONS 126 2.5.4
EQUATION OF MOTION 127 2.6 GRAD S ANALYSIS 127 2.6.1 LIOUVILLE EQUATION
REVISITED 127 2.6.2 TRUNCATED DISTRIBUTIONS 128 2.6.3 GRAD S FIRST AND
SECOND EQUATIONS 129 2.6.4 THE BOLTZMANN EQUATION 130 PROBLEMS 132 THE
BOLTZMANN EQUATION, FLUID DYNAMICS, AND IRREVERSIBILITY 137 3.1
SCATTERING CONCEPTS 138 3.1.1 SEPARATION OF THE HAMILTONIAN 138 3.1.2
SCATTERING ANGLE 140 3.1.3 CROSS SECTION 143 3.1.4 KINEMATICS 146 3.2
THE BOLTZMANN EQUATION 149 3.2.1 COLLISIONAL PARAMETERS AND DERIVATION
149 3.2.2 MULTICOMPONENT GAS 153 3.2.3 REPRESENTATION OF COLLISION
INTEGRAL FOR RIGID SPHERES 153 3.3 FLUID DYNAMIC EQUATIONS AND THE
BOLTZMANN H THEOREM 155 3.3.1 COLLISIONAL INVARIANTS 155 3.3.2
MACROSCOPIC VARIABLES AND CONSERVATIVE EQUATIONS 157 XVI CONTENTS 3.3.3
CONSERVATION EQUATIONS AND THE BOLTZMANN EQUATION 159 3.3.4 TEMPERANCE:
VARIANCE OF THE VELOCITY DISTRIBUTION 161 3.3.5 IRREVERSIBILITY 162
3.3.6 POINCARE RECURRENCE THEOREM 163 3.3.7 BOLTZMANN AND GIBBS
ENTROPIES 164 3.3.8 BOLTZMANN S H THEOREM 166 3.3.9 STATISTICAL BALANCE
167 3.3.10 THE MAXWELLIAN 168 3.3.11 THE BAROMETER FORMULA 170 3.3.12
CENTRAL-LIMIT THEOREM REVISITED 172 3.4 TRANSPORT COEFFICIENTS 174 3.4.1
RESPONSE TO GRADIENT PERTURBATIONS 174 3.4.2 ELEMENTARY MEAN-FREE-PATH
ESTIMATES . . . . . . 178 3.4.3 DIFFUSION AND RANDOM WALK 186 3.4.4
AUTOCORRELATION FUNCTIONS, TRANSPORT COEFFICIENTS, AND KUBO FORMULA 188
3.5 THE CHAPMAN-ENSKOG EXPANSION 194 3.5.1 COLLISION FREQUENCY 194 3.5.2
THE EXPANSION 195 3.5.3 SECOND-ORDER SOLUTION 199 3.5.4 THERMAL
CONDUCTIVITY AND STRESS TENSOR 202 3.5.5 SONINE POLYNOMIALS 203 3.5.6
APPLICATION TO RIGID SPHERES 207 3.5.7 DIFFUSION AND ELECTRICAL
CONDUCTIVITY 208 3.5.8 EXPRESSIONS OF 2 ( I FOR INVERSE POWER
INTERACTION FORCES 209 3.5.9 INTERACTION MODELS AND EXPERIMENTAL VALUES
... 211 3.5.10 THE METHOD OF MOMENTS 213 3.6 THE LINEAR BOLTZMANN
COLLISION OPERATOR 217 3.6.1 SYMMETRY OF THE KERNEL 217 3.6.2 NEGATIVE
EIGENVALUES 218 3.6.3 COMPARISON OF BOLTZMANN AND LIOUVILLE OPERATORS
219 3.6.4 HARD AND SOFT POTENTIALS 220 3.6.5 MAXWELL MOLECULE SPECTRUM
220 3.6.6 FURTHER SPECTRAL PROPERTIES 222 3.7 THE DRUYVESTEYN
DISTRIBUTION 225 3.7.1 BASIC PARAMETERS AND STARTING EQUATIONS 225 3.7.2
LEGENDRE POLYNOMIAL EXPANSION 227 3.7.3 REDUCTION OF 7 O (/O I F) 232
3.7.4 EVALUATION OF 7 0 AND I INTEGRAL S 233 3.7.5 DRUYVESTEYN EQUATION
236 3.7.6 NORMALIZATION, VELOCITY SHIFT, AND ELECTRICAL CONDUCTIVITY 237
CONTENTS XVII 3.8 FURTHER REMARKS ON IRREVERSIBILITY 240 3.8.1
ERGODICFLOW 240 3.8.2 MIXING FLOW AND COARSE GRAINING 243 3.8.3
ACTION-ANGLE VARIABLES 245 3.8.4 HAMILTON-JACOBI EQUATION 248 3.8.5
CONDITIONALLY PERIODIC MOTION AND CLASSICAL DEGENERACY 249 3.8.6 BRUNS S
THEOREM 253 3.8.7 ANHARMONIC OSCILLATOR 253 3.8.8 RESONANT DOMAINS AND
THE KAM THEOREM . . . . 255 PROBLEMS 258 ASSORTED KINETIC EQUATIONS WITH
APPLICATIONS TO PLASMAS AND NEUTRAL FLUIDS 278 4.1 APPLICATION OF THE
VLASOV EQUATION TO A PLASMA 279 4.1.1 DEBYE POTENTIAL AND DIELECTRIC
CONSTANT 279 4.1.2 WAVES, INSTABILITIES, AND DAMPING 285 4.1.3 LANDAU
DAMPING 288 4.1.4 NYQUIST CRITERION 292 4.2 FURTHER KINETIC EQUATIONS OF
PLASMAS AND NEUTRAL FLUIDS . 294 4.2.1 KROOK-BHATNAGER-GROSS EQUATION
295 4.2.2 KBG ANALYSIS OF SHOCK WAVES 298 4.2.3 THE FOKKER-PLANCK
EQUATION 301 4.2.4 THE LANDAU EQUATION 307 4.2.5 THE BALESCU-LENARD
EQUATION . . . 309 4.2.6 CONVERGENT KINETIC EQUATION 315 4.2.7
FOKKER-PLANCK EQUATION REVISITED 317 4.3 MONTE CARLO ANALYSIS IN KINETIC
THEORY 319 4.3.1 MASTER EQUATION 319 4.3.2 EQUIVALENCE OF MASTER AND
INTEGRAL EQUATIONS . . 320 4.3.3 INTERPRETATION OF TERMS 321 4.3.4
APPLICATION OF RANDOM NUMBERS 323 4.3.5 PROGRAM FOR EVALUATION OF
DISTRIBUTION FUNCTION . 324 PROBLEMS 325 ELEMENTS OF QUANTUM KINETIC
THEORY 329 5.1 BASIC PRINCIPLES 330 5.1.1 THE WAVE FUNCTION AND ITS
PROPERTIES 330 5.1.2 COMMUTATORS AND MEASUREMENT 332 5.1.3
REPRESENTATIONS 334 5.1.4 COORDINATE AND MOMENTUM REPRESENTATIONS . . .
335 5.1.5 SUPERPOSITION PRINCIPLE 337 5.1.6 STATISTICS AND THE PAULI
PRINCIPLE 339 5.1.7 HEISENBERG PICTURE 339 5.2 THE DENSITY MATRIX 341
XVIII CONTENTS 5.2.1 THE DENSITY OPERATOR 342 5.2.2 THE PAULI EQUATION
346 5.2.3 THE WIGNER DISTRIBUTION 351 5.2.4 WEYL CORRESPONDENCE 354
5.2.5 WIGNER-MOYAL EQUATION 357 5.2.6 HOMOGENEOUS LIMIT: PAULI EQUATION
REVISITED . . 359 5.3 APPLICATION OF THE KBG EQUATION TO QUANTUM SYSTEMS
. 363 5.3.1 EQUILIBRIUM DISTRIBUTIONS 363 5.3.2 PHOTON KINETIC EQUATION
366 5.3.3 ELECTRON TRANSPORT IN METALS 369 5.3.4 THOMAS-FERMI SCREENING
376 5.3.5 MOTT TRANSITION 378 5.3.6 RELAXATION TIME FOR CHARGE-CARRIER
PHONON INTERACTION 379 5.4 QUANTUM MODIFICATIONS OF THE BOLTZMANN
EQUATION . . . 385 5.4.1 QUASI-CLASSICAL BOLTZMANN EQUATION 385 5.4.2
KINETIC THEORY FOR EXCITATIONS IN A FERMI LIQUID 387 5.4.3 H THEOREM FOR
QUASI-CLASSICAL DISTRIBUTION ... 392 5.5 OVERVIEW OF CLASSICAL AND
QUANTUM HIERARCHIES 394 5.5.1 SECOND QUANTIZATION AND FOCK SPACE 394
5.5.2 CLASSICAL AND QUANTUM DISTRIBUTION FUNCTIONS . . 395 5.5.3
EQUATIONS OF MOTION 399 5.5.4 GENERALIZED HIERARCHIES 400 5.6 KUBO
FORMULA REVISITED 403 5.6.1 CHARGE DENSITY AND CURRENT 403 5.6.2
IDENTIFICATIONS FOR KUBO FORMULA 404 5.6.3 ELECTRICAL CONDUCTIVITY 405
5.6.4 REDUCTION TO DRUDE CONDUCTIVITY 407 5.7 ELEMENTS OF THE GREEN S
FUNCTION FORMALISM 408 5.7.1 SCHRODINGER EQUATION GREEN S FUNCTION 408
5.7.2 THE S-BODY GREEN S FUNCTION 410 5.7.3 AVERAGES AND THE GREEN S
FUNCTION 410 5.7.4 THE QUASI-FREE PARTICLE 413 5.7.5 ONE-BODY GREEN S
FUNCTION 414 5.7.6 RETARDED AND ADVANCED GREEN S FUNCTIONS . . . . 415
5.7.7 COUPLED GREEN S FUNCTION EQUATIONS 415 5.7.8 DIAGRAMS AND
EXPANSION TECHNIQUES 416 5.8 SPECTRAL FUNCTION FOR ELECTRON-PHONON
INTERACTIONS ... 421 5.8.1 HAMILTONIAN 421 5.8.2 GREEN S FUNCTION
EQUATIONS OF MOTION 423 5.8.3 THE SPECTRAL FUNCTION 425 5.8.4 LORENTZIAN
FORM 426 5.8.5 LIFETIME AND ENERGY OF A QUASI-FREE PARTICLE . . 428
PROBLEMS 429 CONTENTS XIX 6 RELATIVISTIC KINETIC THEORY 449 6.1
PRELIMINARIES : 450 6.1.1 POSTULATES 450 6.1.2 EVENTS, WORLD LINES, AND
THE LIGHT CONE 450 6.1.3 FOUR-VECTORS 451 6.1.4 LORENTZ TRANSFORMATION
452 6.1.5 LENGTH CONTRACTION, TIME DILATION, AND PROPER TIME 454 6.1.6
COVARIANCE, HAMILTONIAN, AND HAMILTON S EQUATIONS 454 6.1.7 CRITERION
FOR RELATIVISTIC ANALYSIS 455 6.2 COVARIANT KINETIC FORMULATION 456
6.2.1 DISTRIBUTION FUNCTION 456 6.2.2 ONE-PARTICLE LIOUVILLE EQUATION
457 6.2.3 COVARIANT ELECTRODYNAMICS 458 6.2.4 VLASOV EQUATION 459 6.2.5
COVARIANT DRUDE FORMULATION OF OHM S LAW . . . 460 6.2.6 LORENTZ
INVARIANTS IN KINETIC THEORY 461 6.2.7 RELATIVISTIC ELECTRON GAS AND
DARWIN LAGRANGIAN 464 6.3 THE RELATIVISTIC MAXWELLIAN 467 6.3.1
NORMALIZATION 467 6.3.2 THE NONRELATIVISTIC DOMAIN 469 6.4 NON-CARTESIAN
COORDINATES 470 6.4.1 COVARIANT AND CONTRAVARIANT VECTORS 470 6.4.2
METRIC TENSOR 471 6.4.3 LAGRANGE S EQUATIONS 472 6.4.4 THE CHRISTOFFEL
SYMBOL 473 6.4.5 LIOUVILLE EQUATION 474 PROBLEMS 474 7 KINETIC
PROPERTIES OF METALS AND AMORPHOUS MEDIA 480 7.1 METALLIC ELECTRICAL AND
THERMAL CONDUCTION 482 7.1.1 BACKGROUND 482 7.1.2 THERMOPOWER 484 7.1.3
ELECTRON-PHONON SCATTERING MATRIX ELEMENTS . . 487 7.1.4 QUANTUM
BOLTZMANN EQUATION 493 7.1.5 PERTURBATION DISTRIBUTION 496 7.1.6
ELECTRICAL RESISTIVITY 498 7.1.7 SCALE PARAMETERS OF P 0 503 7.1.8
ELECTRON DISTRIBUTION FUNCTION 504 7.1.9 THERMAL CONDUCTIVITY 504 7.2
AMORPHOUS MEDIA 505 7.2.1 BACKGROUND 505 7.2.2 LOCALIZATION 508 7.2.3
CONDUCTION MECHANISMS AND HOPPING 511 XX CONTENTS 7.2.4 PERCOLATION
PHENOMENA 514 7.2.5 PAIR-CONNECTEDNESS FUNCTION AND SCALING .... 517
7.2.6 LOCALIZATION IN SECOND QUANTIZATION 520 PROBLEMS 524 LOCATION OF
KEY EQUATIONS 527 LIST OF SYMBOLS 529 APPENDICES A VECTOR FORMULAS AND
TENSOR NOTATION 537 A.I DEFINITIONS 537 A.2 VECTOR FORMULAS AND TENSOR
EQUIVALENTS 539 B MATHEMATICAL FORMULAS 541 B.I TENSOR INTEGRALS AND
UNIT VECTOR PRODUCTS 541 B.2 EXPONENTIAL INTEGRAL, F FUNCTION,
FUNCTION, AND ERROR FUNCTION 542 B.2.1 EXPONENTIAL INTEGRAL 542 B.3
OTHER USEFUL INTEGRALS 545 B .4 HERMITE AND LAGUERRE POLYNOMIALS AND THE
HYPERGEOMETRIC FUNCTION 546 C PHYSICAL CONSTANTS 550 D LORENTZ-LEGENDRE
EXPANSION 552 E ADDITIONAL REFERENCES 554 E.I EARLY WORKS 554 E.2 RECENT
CONTRIBUTIONS TO KINETIC THEORY AND ALLIED TOPICS 558 F SCIENCE AND
SOCIETY IN THE CLASSICAL GREEK AND ROMAN ERAS 563 INDEX 565
|
| any_adam_object | 1 |
| author | Liboff, Richard L. |
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| author_sort | Liboff, Richard L. |
| author_variant | r l l rl rll |
| building | Verbundindex |
| bvnumber | BV017575005 |
| callnumber-first | Q - Science |
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| callnumber-sort | QC 3174.9 |
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| classification_rvk | UF 1950 |
| classification_tum | PHY 058f |
| ctrlnum | (OCoLC)50064639 (DE-599)BVBBV017575005 |
| dewey-full | 530.13/6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.13/6 |
| dewey-search | 530.13/6 |
| dewey-sort | 3530.13 16 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| edition | 3. ed. |
| format | Book |
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| id | DE-604.BV017575005 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:19:28Z |
| institution | BVB |
| isbn | 0387955518 9780387955513 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010574797 |
| oclc_num | 50064639 |
| open_access_boolean | |
| owner | DE-703 DE-91G DE-BY-TUM DE-11 DE-19 DE-BY-UBM |
| owner_facet | DE-703 DE-91G DE-BY-TUM DE-11 DE-19 DE-BY-UBM |
| physical | XX, 571 S. graph. Darst. : 24 cm |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Springer |
| record_format | marc |
| series2 | Graduate texts in contemporary physics |
| spelling | Liboff, Richard L. Verfasser aut Kinetic theory classical, quantum, and relativistic descriptions Richard L. Liboff 3. ed. New York [u.a.] Springer 2003 XX, 571 S. graph. Darst. : 24 cm txt rdacontent n rdamedia nc rdacarrier Graduate texts in contemporary physics Literaturverz. S. 558 - 562 Kinetic theory of matter Kinetische Theorie (DE-588)4030669-0 gnd rswk-swf Kinetik (DE-588)4030665-3 gnd rswk-swf Kinetische Theorie (DE-588)4030669-0 s DE-604 Kinetik (DE-588)4030665-3 s 1\p DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010574797&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Liboff, Richard L. Kinetic theory classical, quantum, and relativistic descriptions Kinetic theory of matter Kinetische Theorie (DE-588)4030669-0 gnd Kinetik (DE-588)4030665-3 gnd |
| subject_GND | (DE-588)4030669-0 (DE-588)4030665-3 |
| title | Kinetic theory classical, quantum, and relativistic descriptions |
| title_auth | Kinetic theory classical, quantum, and relativistic descriptions |
| title_exact_search | Kinetic theory classical, quantum, and relativistic descriptions |
| title_full | Kinetic theory classical, quantum, and relativistic descriptions Richard L. Liboff |
| title_fullStr | Kinetic theory classical, quantum, and relativistic descriptions Richard L. Liboff |
| title_full_unstemmed | Kinetic theory classical, quantum, and relativistic descriptions Richard L. Liboff |
| title_short | Kinetic theory |
| title_sort | kinetic theory classical quantum and relativistic descriptions |
| title_sub | classical, quantum, and relativistic descriptions |
| topic | Kinetic theory of matter Kinetische Theorie (DE-588)4030669-0 gnd Kinetik (DE-588)4030665-3 gnd |
| topic_facet | Kinetic theory of matter Kinetische Theorie Kinetik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010574797&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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