Equilibrium and non-equilibrium statistical mechanics/ (Record no. 185918)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 00383nam a2200133Ia 4500 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9789812704788 |
| 040 ## - CATALOGING SOURCE | |
| Transcribing agency | CUS |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 530.13 |
| Item number | VLI/E |
| 100 ## - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Vliet, Carolyne M. Van. |
| 245 #0 - TITLE STATEMENT | |
| Title | Equilibrium and non-equilibrium statistical mechanics/ |
| Statement of responsibility, etc. | Carolyne M. Van Vliet |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Place of publication, distribution, etc. | New Jersey: |
| Name of publisher, distributor, etc. | World Scientific Pub., |
| Date of publication, distribution, etc. | 2008. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | xxvi, 960 p. : |
| Other physical details | ill. ; |
| Dimensions | 27 cm. |
| 505 ## - FORMATTED CONTENTS NOTE | |
| Formatted contents note | PREFACE vii<br/>E Q U I L I B R I U M S T A T I S T I C A L M E C H A N I C S<br/>PART A. GENERAL PRINCIPLES OF MANY-PARTICLE SYSTEMS<br/>Chapter I. Introduction to the State of Large Systems and some Probability<br/>Concepts 5<br/>1.1 Purpose of statistical mechanics for classical and quantum systems 5<br/>1.2 Gamma-space and its quantum equivalent 8<br/>1.3 The thermodynamic state 12<br/>1.3.1 Macroscopic thermodynamics; Callen's entropy 12<br/>1.3.2 Statistical mechanical state functions; Gibbs' entropy 15<br/>1.4 Various ensembles and their main state functions 17<br/>1.5 Fluctuating state variables; the a- space 18<br/>1.6 Some mathematical distribution functions 20<br/>1.6.1 The binomial distribution and random walk 20<br/>1.6.2 The multinomial distribution function 24<br/>1.6.3 The Poisson distribution, Gauss distribution and normal distribution 25<br/>1.6.4 Multivariate distributions, the Maxwell¿Boltzmann distribution and<br/>the virial theorem 28<br/>1.7 Transforms of probability functions 33<br/>1.7.1 Characteristic functions 33<br/>1.7.2 The generating function according to Laplace 37<br/>1.7.3 The factorial moment generating function, Fowler transform and<br/>cumulants 38<br/>1.7.4 The Mellin transform 42<br/>1.8 Problems to Chapter I 43<br/>Chapter II. Statistics of Closed Systems 46<br/>2.1 Liouville's theorem and the microcanonical density function 46<br/>2.2 The ergodic hypothesis 48<br/>2.3 Von Neumann's theorem and the microcanonical density operator 50<br/>Table of Contents<br/>xiv<br/>2.4 Macro-probability in classical and quantum statistics 53<br/>2.5 Examples of extension in phase space and accessible number of quantum<br/>states 56<br/>2.5.1 Ideal gas 56<br/>2.5.2 An assembly of oscillators; 58<br/>2.5.3 A general form for ??(E,V,N) in the microcanonical ensemble 61<br/>2.6 Problems to Chapter II 63<br/>Chapter III. Thermodynamics in the Microcanonical Ensemble, Classical<br/>and Quantal 65<br/>3.1 Gibbs' form of the ergodic density; entropy for classical systems 65<br/>3.2 Entropy for quantum systems 69<br/>3.3 The equipartition law 71<br/>3.4 Various forms for the entropy in closed and in open systems; 73<br/>3.5 Properties of entropy 74<br/>3.5.1 Elementary entropies, Sackur¿Tetrode formula 74<br/>3.5.2 Homogeneous entropy form and Gibbs¿Duhem relation 77<br/>3.5.3 Maxwell relations 78<br/>3.5.4 Nernst¿s law and statistical mechanics 79<br/>3.6 Equilibrium and local stability requirements 81<br/>3.7 Entropy and probability 83<br/>3.7.1 Boltzmann¿s principle 84<br/>3.7.2 The Boltzmann-Einstein principle 84<br/>3.8 The Gibbs entropy function 85<br/>3.8.1 Gibbs¿ entropy function for a nonequilibrium state 85<br/>3.8.2 Failure for the second law of thermod. in precisely defined microstate 86<br/>3.8.3 Coarse-graining and the second law 87<br/>3.8.4 Fluctuations of extensive and intensive variables 88<br/>3.9 Problems to Chapter III 91<br/>Chapter IV. Ensembles in the Presence of Reservoirs: The Canonical<br/>and Grand-Canonical Ensemble 93<br/>1. GENERAL FORMALISM AND SOME QUANTUM APPLICATIONS<br/>4.1 The canonical ensemble for systems in contact with a heat bath 93<br/>4.2 The grand-canonical ensemble for systems with energy / particle exchange 96<br/>4.3 Quantum Illustrations of the canonical and grand-canonical distribution 102<br/>4.3.1 The Fermi¿Dirac and Bose¿Einstein results 102<br/>4.3.2 The one-dimensional Ising model 105<br/>Table of Contents<br/>xv<br/>2. DENSE CLASSICAL GASES AND FURTHER APPLICATIONS<br/>4.4 Second virial coefficient for a classical gas and van der Waals¿ law 108<br/>4.4.1 Ornstein¿s method as elaborated by van Kampen 109<br/>4.4.2 Van der Waals¿ equation; fluctuations and pair correlation function 112<br/>4.4.3 Cluster-integral method 117<br/>4.5 Tonk¿s hard-core gas and Takahashi¿s nearest neighbour gas 120<br/>4.6 The method of steepest descent 124<br/>4.7 Dense gases and the virial coefficients via the grand-canonical ensemble 127<br/>4.7.1 Cluster expansion 127<br/>4.7.2 Cumulant expansion 133<br/>4.8 Mean-field theories 135<br/>4.8.1 The Ising Hamiltonian and the Weiss molecular field 135<br/>4.8.2 The Bragg¿Williams method. Order-disorder transitions 137<br/>4.9 Landau¿Ginzburg theory for phase transitions; ?-points 145<br/>4.9.1 General procedure 145<br/>4.9.2 Classification of phase transitions 147<br/>4.10 Ionized gases ¿ plasmas ¿ or electron-hole gases in condensed matter 150<br/>4.10.1 Coulomb interactions. The Debye¿Hückel theory 150<br/>4.10.2 Coulomb interactions via the pair-dist. function; BBGK hierarchy 154<br/>4.11 Distribution functions, correlation functions and covariance functions 157<br/>4.12 Problems to Chapter IV 163<br/>Chapter V. Generalized Canonical Ensembles 170<br/>5.1 Formal results 170<br/>5.1.1 The generalized ensemble probability 170<br/>5.1.2 Thermodynamic functions 173<br/>5.1.3 The macroscopic thermodynamic distribution 174<br/>5.2 Transformation theory using the Fowler generating function 175<br/>5.3 Fluctuations: general results 177<br/>5.3.1 Extensive variables 177<br/>5.3.2 Intensive variables 179<br/>5.3.3 Examples and conclusions 181<br/>5.4 Carrier-density fluctuations in a solid 183<br/>5.4.1 Microscopic occupancy fluctuations 183<br/>5.4.2 Macroscopic occupancy fluctuations 185<br/>5.4.3 Examples for non-degenerate and degenerate semiconductors 186<br/>5.5 Fluctuations in systems interacting with finite reservoirs 189<br/>5.6 Alternate Fermi¿Dirac distributions 191<br/>5.7 Problems to Chapter V 195<br/>Table of Contents<br/>xvi<br/>PART B. CLASSICAL AND QUANTUM FORMALISMS. THE<br/>BOLTZMANN GAS, THE PERFECT BOSE GAS AND FERMI GAS<br/>Chapter VI. The Boltzmann Distribution and Chemical Applications 201<br/>6.1 Aspects of molecular distributions 201<br/>6.2 The Darwin¿Fowler procedure 204<br/>6.3 Thermodynamic functions and standard forms 206<br/>6.4 Fluctuations of the distribution function 208<br/>6.5 Classical Illustrations 210<br/>6.5.1 Effect of a magnetic field; Bohr-van Leeuwen theorem 210<br/>6.5.2 Generalized Sackur¿Tetrode formula and the equations of state 211<br/>6.6 Oscillators 213<br/>6.6.1 The Planck oscillator 213<br/>6.6.2 The Fermi oscillator 214<br/>6.7 Rotators 215<br/>6.8 Dielectric and paramagnetic dipoles 221<br/>6.9 Chemical equilibrium and the mass-action law 223<br/>6.10 Problems to Chapter VI 226<br/>Chapter VII. The Occupation-Number State Formalism; Spin and 228<br/>Statistics<br/>7.1 Symmetrization of states 228<br/>7.2 Systems of bosons. Creation and annihilation operators 231<br/>7.3 Many-body boson operators 234<br/>7.3.1 Expressions in terms of , ¿ k k a a 234<br/>7.3.2 Field operators and local variables 238<br/>7.4 On the quantization of fields 242<br/>7.5 Fermion operators; anticommutation rules 246<br/>7.6 Many-body fermion operators 250<br/>7.6.1 Expressions in terms of , ¿ k k c c 250<br/>7.6.2 Field operators; spin 252<br/>7.7 The boson-fermion dichotomy: general remarks 253<br/>7.8 The Hartree¿Fock equation* 254<br/>7.9 Problems to Chapter VII 258<br/>Chapter VIII. Ideal Quantum Gases and Elementary Excitations in Solids 260<br/>8.1 Bose Einstein statistics for zero-restmass particles; blackbody radiation 260<br/>8.1.1 Planck¿s law; original considerations 260<br/>Table of Contents<br/>xvii<br/>8.1.2 Quantization of the electromagnetic field; photons 262<br/>8.2 The perfect Bose gas 265<br/>8.3 Bose¿Einstein condensation 269<br/>8.3.1 The P-v¿ and the P-Tdiagram 269<br/>8.3.2 Coexisting phases and thermodynamic functions 272<br/>8.4 The perfect Fermi gas 275<br/>8.5 Lattice vibrations; phonons 280<br/>8.5.1 Continuum description. Einstein and Debye specific heat 280<br/>8.5.2 Normal modes; running-wave boson operators 282<br/>8.6 Elements of electron-phonon interaction 288<br/>8.7 Problems to Chapter VIII 295<br/>PART C. QUANTUM SYSTEMS WITH STRONG INTERACTIONS<br/>Chapter IX. Critical Phenomena: General Features of Phase Transitions 301<br/>9.1 Introductory remarks 301<br/>9.2 Critical fluctuations 302<br/>9.2.1 Elements of functional theory 302<br/>9.2.2 Landau-Ginzburg density functionals 304<br/>9.2.3 Spatial correlation function 306<br/>9.3 Critical exponents and scaling relations 309<br/>9.4 Thermodynamic inequalities 313<br/>9.4.1 Magnetic systems; the Curie-point transition 313<br/>9.4.2 Vapour-liquid transition and the coexistence region 315<br/>9.5 Dimensional analysis 318<br/>9.6 Other scaling hypotheses 319<br/>9.6.1 Widom scaling 319<br/>9.6.2 Kadanoff scaling 321<br/>9.7 Other topics in phase transitions 324<br/>9.7.1 Symmetry breaking and order parameters 324<br/>9.7.2 The tricritical point 326<br/>9.7.3 The Ginzburg criterion 330<br/>9.7.4 The Kosterlitz¿Thouless transition 331<br/>9.8 Problems to Chapter IX 334<br/>Chapter X. Renormalization: Theory and Examples 338<br/>10.1 Objective of renormalization 338<br/>10.2 The linear spin chain revisited 339<br/>Table of Contents<br/>xviii<br/>10.3 The renormalization group 343<br/>10.3.1 Fixed points, infinitesimal transformations and scaling fields 343<br/>10.3.2 Connection with Widom¿s scaling function; critical exponents 347<br/>10.4 Niemeijer¿van Leeuwen cumulant expansion for triangular lattice 348<br/>10.4.1 First-order results 350<br/>10.4.2 Higher-order results 353<br/>10.5 The ¿classical spin¿ Gaussian model 356<br/>10.6 Elements of the S4 model and the epsilon expansion 361<br/>10.7 Problems to Chapter X 370<br/>Chapter XI. The Two-dimensional Ising Model and Spin Waves 372<br/>11.1 Historical notes. Review of the 1D model 372<br/>11.2 The transfer matrix for the rectangular lattice 376<br/>11.2.1 Procedure 376<br/>11.2.2 Transformation to an interacting fermion problem 378<br/>11.2.3 Running-wave fermion operators 381<br/>11.2.4 Bogoliubov¿Valatin transformation 386<br/>11.3 The critical temperature and the thermodynamic functions 387<br/>11.4 The spontaneous magnetization 395<br/>11.4.1 Spin-spin correlation function 395<br/>11.4.2 Evaluation of the Toeplitz determinant; Onsager¿s result 400<br/>11.5 Ferromagnetism as excitation of magnons 403<br/>11.6 Bose¿Einstein statistics for magnons 406<br/>11.7 The Heisenberg antiferromagnet 408<br/>11.8 Problems to Chapter XI 412<br/>Chapter XII. Aspects of Quantum Fluids 415<br/>1. VARIOUS SPECIAL THEORIES<br/>12.1 Superfluidity; general features 415<br/>12.2 Elements of Feynman¿s theory 421<br/>12.2.1 The ground state and single-quantum excited state 421<br/>12.2.2 The excitation spectrum for T > 0 423<br/>12.3 Bogoliubov¿s theory of excitations in 4He 426<br/>12.3.1 The grand Hamiltonian 426<br/>12.3.2 The chemical potential 431<br/>12.4 Gaseous atomic Bose¿Einstein condensates 433<br/>12.4.1 Quantum equations for the near-perfect B¿E gas 434<br/>12.4.2 Properties and solutions of the Gross¿Pitaevskii equation 436<br/>Table of Contents<br/>xix<br/>12.5 Superconductivity 440<br/>12.5.1 The Fröhlich Hamiltonian 440<br/>12.5.2 Cooper pairs 443<br/>12.6 The BCS Hamiltonian 445<br/>12.6.1 The ground state 445<br/>12.6.2 Finite temperature results 450<br/>12.7 Excitations in Fermi liquids; 3He 455<br/>12.7.1 Original Fermi liquid theory (Landau) and some empirical data 455<br/>12.7.2 The ground state and pair-correlation function 465<br/>12.8 Modern developments of 3He 467<br/>12.8.1 Other excitations 467<br/>12.8.2 Balian¿Werthamer (BW) Hamiltonian for the superfluid phases 470<br/>2. FORMAL THEORY; DIAGRAMMATIC METHODS<br/>12.9 Perturbation expansion of the grand-canonical partition function 474<br/>12.9.1 The interaction picture; expansion of the evolution operator 474<br/>12.9.2 Generalized Wick¿s theorem 478<br/>12.10 Momentum-space diagrams 481<br/>12.10.1 Feynman diagrams 482<br/>12.10.2 Hugenholtz diagrams 487<br/>12.10.3 Fourier-transformed frequency diagrams 490<br/>12.11 Full Propagators (or Green¿s functions) for normal quantum fluids 494<br/>12.11.1 Spatial and momentum forms 494<br/>12.11.2 Cumulant expansion of the Green¿s function in free propagators 499<br/>12.12 Self-energy and Dyson¿s equation 502<br/>12.13 Fermi liquids revisited 506<br/>12.13.1 The Hartree¿Fock approximation 506<br/>12.13.2 The ring approximation (RPA) 513<br/>(a) Classical electron gas with positive charge background 518<br/>(b) Quantum electron gas near T = 0 520<br/>12.14 Problems to Chapter XII 523<br/>Table of Contents<br/>xx<br/>N O N - E Q U I L I B R I U M S T A T I S T I S T I C A L<br/>M E C H A N I C S<br/>PART D. CLASSICAL TRANSPORT THEORY<br/>Chapter XIII. The Boltzmann Equation and Boltzmann¿s ?-Theorem 531<br/>13.1 Introduction to Boltzmann theory 531<br/>13.2 The Boltzmann equation in velocity-position space 533<br/>13.3 The Boltzmann equation for solids with extended states 538<br/>13.4 Connection with the cross section; examples of ?(?) 543<br/>13.4.1 Matrix element squared ??cross section 543<br/>13.4.2 Classical and quantum mechanical examples of ?(?) 545<br/>13.5 Boltzmann¿s H-theorem 550<br/>13.5.1 Derivation 550<br/>13.5.2 Further discussion of Boltzmann¿s H-theorem 554<br/>13.6 The equilibrium solutions 556<br/>13.6.1 The classical gas 556<br/>13.6.2 Quantum gases 556<br/>13.7 The equilibrium entropy 558<br/>13.8 Problems to Chapter XIII 561<br/>Chapter XIV. Hydrodynamic Equations and Conservation Theorems,<br/>Barycentric Flow 563<br/>14.1 Conservation theorems 563<br/>14.1.1 Full theorems 563<br/>14.1.2 Zero-order or Eulerian conservation theorems 569<br/>14.2 The phenomenological equations in classical systems 571<br/>14.2.1 The basis of the flow problem 571<br/>14.2.2 Relaxation-time model 574<br/>14.2.3 Computation of the vector and tensor flow averages in systems<br/>with barycentric flow 576<br/>14.3 The hydrodynamic equations 581<br/>14.4 Computation of the entropy production 584<br/>14.5 Problems to Chapter XIV 588<br/>Chapter XV. Further Applications 589<br/>1. NEAR-EQUILIBRIUM TRANSPORT<br/>Table of Contents<br/>xxi<br/>15.1 Electron gas in metals: the perturbation description 589<br/>15.2 The streaming-vector method 592<br/>15.2.1 Fluxes in the absence of a magnetic field 592<br/>15.2.2 Incorporation of a magnetic field 596<br/>15.3 Entropy production and heat flux 599<br/>15.4 The phenomenological equations for solids 601<br/>15.4.1 General scheme 601<br/>15.4.2 Galvanomagnetic and thermomagnetic effects 603<br/>15.5 Mobility computations* 607<br/>15.5.1 Resistivity of metals; Bloch¿s formula 607<br/>15.5.2 Acoustic phonon scattering in nondegenerate semiconductors 612<br/>2. TRANSPORT FAR FROM EQUILIBRIUM; STEADY-STATE DISTRIBUTIONS AND FLOW<br/>15.6 The coupled Boltzmann equations in the v-language; expansion in<br/>spherical polynomials 615<br/>15.7 The zero-order and first-order collision integrals in a binary plasma 619<br/>15.8 Electron heating in plasmas: the Druyvesteyn distribution 621<br/>15.9 Coupled Boltzmann equations for hot electrons in semiconductors 623<br/>15.10 The steady-state distribution for a hot electron gas 624<br/>15.11 Transport in hot electron systems 630<br/>15.12 Problems to Chapter XV 632<br/>PART E. LINEAR RESPONSE THEORY AND QUANTUM TRANSPORT<br/>Chapter XVI. Linear Response Theory, Reduced Operators and<br/>Convergent Forms 637<br/>1. THE ORIGINAL KUBO¿GREEN FORMALISM<br/>16.1 Introduction to linear response theory 637<br/>16.2 The response function and the relaxation function 639<br/>16.3 The frequency domain; various forms 644<br/>16.3.1 The commutator form 644<br/>16.3.2 The Kubo form and the Fujita form 646<br/>16.3.3 The correlation form 648<br/>16.3.4 The fluctuation-dissipation theorem 650<br/>16.4 The Wiener¿Khintchine theorem 654<br/>16.5 Density-density correlations and the dynamic structure factor 657<br/>16.5.1 General considerations 657<br/>Table of Contents<br/>xxii<br/>16.5.2 Another form of the fluctuation-dissipation theorem 660<br/>16.5.3 Thermodynamics and sum-rules 661<br/>16.6 A return to quantum liquids 664<br/>16.6.1 Self-consistent field approximation 664<br/>16.6.2 Excitations in the Bose liquid 666<br/>16.6.3 Fermi liquids 668<br/>16.6.4 Real time Green¿s functions and the diagrammatic evaluation 672<br/>16.7 Kubo-theory conductivity computations 674<br/>16.8 Criticism of linear response theory 677<br/>16.8.1 Van Kampen¿s objections 677<br/>16.8.2 Our criticism 678<br/>2. REDUCED OPERATORS AND CONVERGENT FORMS<br/>16.9 The master operator in Liouville space 679<br/>16.9.1 Results for small times 681<br/>16.9.2 Results for large times 685<br/>16.10 Irreversible transport equations via projector operators 686<br/>16.10.1 Some theorems 686<br/>16.10.2 Reduction of the Heisenberg equation of motion; diagonal part 689<br/>16.10.3 The full reduced Heisenberg equation and the current operator 692<br/>16.10.4 Consequences for the many-body response formulae 696<br/>16.11 The Pauli¿Van Hove master equation 698<br/>16.12 The full master equation (FME) 701<br/>16.13 Approach to equilibrium 704<br/>16.14 The Onsager¿Casimir reciprocity relations 705<br/>16.14.1 The diagonal correlation functions 705<br/>16.14.2 The nondiagonal correlation functions 708<br/>16.14.3 Some lemmas 710<br/>16.15 An exact response result: Cohen¿Van Vliet 711<br/>16.16 Problems to Chapter XVI 715<br/>Chapter XVII. The Quantum Boltzmann Equation and Some Applications 719<br/>1. THE QUANTUM BOLTZMANN EQUATION: SCOPE AND ESSENCE<br/>17.1 From the master equation to the quantum Boltzmann equation 719<br/>17.1.1 The quantum Boltzmann equation for binary interactions 720<br/>17.1.2 The quantum Boltzmann equation for electron-phonon interaction 724<br/>17.2 Discussion of the equilibrium and steady-state distribution 725<br/>17.3 Extended states. Recovery of the BTE via the Wigner formalism 727<br/>Table of Contents<br/>xxiii<br/>17.4 Generalized Calecki equation for the nonlinear current flux 731<br/>17.5 The linearized quantum Boltzmann equation* 732<br/>17.6 Electrical Conductivities in the linear regime* 735<br/>17.6.1 Ponderomotive conductivities 736<br/>17.6.2 The Argyres¿Roth formula for the collisional conductivity 738<br/>17.7 Localised states: a direct perturbation treatment 739<br/>17.8 Diagonal and nondiagonal conductivities from modified LRT 741<br/>2. SOME APPLICATIONS OF MODIFIED LINEAR RESPONSE THEORY<br/>17.9 Landau states: 3D applications 744<br/>17.9.1 The ordinary Hall effect 744<br/>17.9.2 Transverse magnetoresistance 747<br/>17.10 Landau States: 2D and 1D applications 749<br/>17.10.1 The quantum Hall effect 749<br/>17.10.2 Magnetophonon resonances 752<br/>17.11 Slightly disordered metals. The Aharonov¿Bohm effect 760<br/>17.11.1 Landauer¿Büttiker models 763<br/>17.11.2 Diagrammatic methods 764<br/>17.11.3 Modified LRT results 765<br/>3. THE MASTER HIERARCHY<br/>17.12 Kinetic Equations for quantum systems with binary interactions 771<br/>17.12.1 Fermion moment equations and Fokker¿Planck moments 771<br/>17.12.2 Boson moment equations 777<br/>17.13 Problems to Chapter XVII 778<br/>PART F. STOCHASTIC PHENOMENA<br/>Chapter XVIII. Brownian Motion and the Mesoscopic Master Equation 781<br/>18.1 Introduction to fluctuations and stochastic phenomena 781<br/>1. THE MESOSCOPIC MASTER EQUATION AND THE MOMENT EQUATIONS<br/>18.2 Probabilistic description of Ornstein and Burger 783<br/>18.2.1 Purely random processes 783<br/>18.2.2 Markovian random processes 784<br/>18.3 Derivation of the mesoscopic master equation 786<br/>Table of Contents<br/>xxiv<br/>18.4 The Kramers¿Moyal expansion and the Fokker¿Planck equation 789<br/>18.5 The phenomenological equations and the fluctuation-relaxation theorem 790<br/>18.5.1 One-variable master equation; birth-death rate processes 795<br/>18.5.2 Multivariate gain-loss processes 798<br/>18.5.3 Electronic fluctuations out of equilibrium 800<br/>18.5.4 Fluctuations about the hydrodynamic state; Brillouin scattering 804<br/>18.6 The Langevin equation 805<br/>18.6-1 General procedure 805<br/>18.6.2 The sources of gain-loss processes and of G-R noise 809<br/>2. BROWNIAN MOTION PROPER. VELOCITY FLUCTUATIONS AND DIFFUSION<br/>18.7 Diffusion and random walk 811<br/>18.7.1 Einstein¿s result 811<br/>18.7.2 Langevin approach of Uhlenbeck and Ornstein 812<br/>18.7.3 Fokker¿Planck solution for the bivariate process{v(t),r(t)} 813<br/>18.7.4 Harmonically bound Brownian particle 816<br/>18.8 Velocity fluctuations and diffusion in condensed matter 817<br/>3. SPECTRAL ANALYSIS<br/>18.9 Overview and Wiener¿Khintchine theorem 821<br/>18.10 The short-time average. MacDonald¿s theorem and Milatz¿ theorem 822<br/>18.10.1 Application to shot noise and similar phenomena 824<br/>18.10.2 Modulated emission noise and wave-interaction noise 826<br/>18.11 Method of elementary events. Campbell¿s and Carson¿s theorems 829<br/>18.12 The Allan-variance theorem 833<br/>18.12.1 Inversion of the Allen variance theorem 836<br/>18.12.2 Counting experiments; non-adjacent sampling 840<br/>18.13 On the origin of 1/f-like noise 842<br/>18.13 The spectra of G-R noise 843<br/>18.13.1 Three-level systems 843<br/>18.14.2 General structure of multi-level G-R noise 850<br/>18.14 Problems to Chapter XVIII 854<br/>Chapter XIX. Branching Processes and Continuous Stochastic Processes 857<br/>1. THE COMPOUNDING THEOREM AND APPLICATIONS<br/>19.1 The compounding theorem, variance theorem and addition theorem 857<br/>19.2 Bernoulli and geometric compounding 860<br/>Table of Contents<br/>xxv<br/>2. METHOD OF RECURRENT GENERATING FUNCTIONS<br/>19.3 Preamble 864<br/>19.4 Singly-incited branching processes. One-carrier avalanche 865<br/>19.5 Doubly-incited branching processes. Two-carrier avalanche 869<br/>3. TRANSPORT FLUCTUATIONS<br/>19.6 On the two Green¿s function procedures for transport noise 877<br/>19.6.1 The correlation method and uniqueness 878<br/>19.6.2 The response form or Langevin form 883<br/>19.7 Applications: Rayleigh diffusion and ambipolar sweep-out 885<br/>19.8 Inhomogeneous systems, effect of boundary terms, examples 890<br/>19.9 Problems to Chapter XIX 896<br/>Chapter XX. Stochastic Optical Signals and Photon Fluctuations 898<br/>20.1 Introductory remarks 898<br/>20.2 Analytic signals and coherence 900<br/>20.3 The quantum field 905<br/>20.4 The pseudo-classical field 907<br/>20.4.1 Sudarshan¿Glauber transform of the statistical density operator 907<br/>20.4.2 Pseudo-classical form of the coherence tensors 908<br/>20.5 Examples for thermal and non-thermal radiation fields 910<br/>20.6 Photon counting. Theory and some experimental results 917<br/>20.7 Problems to Chapter XX 922<br/>Appendix A. The Schrödinger, Heisenberg and Interaction Pictures 923<br/>A.1 Schrödinger form 923<br/>A.2 The Heisenberg picture and connection with classical mechanics 924<br/>A.3 The interaction picture 926<br/>Appendix B. Spin and Statistics 929<br/>B.1 Generalities on fields 930<br/>B.2 Statistics for a scalar spin-zero field 933<br/>B.3 The connection for a field of general spin 935<br/>AUTHOR INDEX 941<br/>SUBJECT INDEX 947 |
| 650 ## - SUBJECT | |
| Keyword | Nonequilibrium statistical mechanics |
| 650 ## - SUBJECT | |
| Keyword | Quantum statistics |
| 650 ## - SUBJECT | |
| Keyword | Statistical mechanics |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | General Books |
| Withdrawn status | Lost status | Damaged status | Not for loan | Home library | Current library | Shelving location | Date acquired | Full call number | Accession number | Date last seen | Date last checked out | Koha item type | Public note |
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| Science Library, Sikkim University | Science Library, Sikkim University | Science Library General Section | 29/08/2016 | 530.13 VLI/E | P40931 | 25/07/2019 | 25/07/2019 | General Books Science Library | Books For SU Science Library |