THE ELEMENTS OF PHYSICS
CONTENTS 1 PROBABILITY, INFORMATION AND PHYSICS INTRODUCTION THEORY OF PROBABILITY LOGICAL FOUNDATIONS OF THE THEORY OF PROBABILITY PRINCIPLES OF STATISTICAL DESCRIPTION STOCHASTIC PROCESSES AND PROBABILITY NORMAL OR GAUSSIAN DISTRIBUTION POISSON DISTRIBUTION THE MEANING OF PROBABILITY INFORMATION AND PROBABILITY ENTROPY AND INFORMATION THEORY BIOGRAPHY OF A N KOLMOGOROV 2 DYNAMICS OF PARTICLES CLASSICAL DYNAMICS QUANTUM MECHANICS AND DYNAMICS STATES AND OBSERVABLES THE SCHR¨ODINGER EQUATION EXPECTATION VALUES OF OBSERVABLES PROBABILITY AND NORMALIZATION OF THE WAVE FUNCTIONS GRAM–SCHMIDT ORTHOGONALIZATION PROCEDURE EVOLUTION OF QUANTUM SYSTEM TIME EVOLUTION AND STATIONARY STATES DYNAMICAL BEHAVIOR OF QUANTUM SYSTEM THE DENSITY OPERATOR THE CHANGE IN TIME OF THE DENSITY MATRIX THE EHRENFEST THEOREM BIOGRAPHY OF ERWIN SCHR¨ODINGER 3 PERTURBATION THEORY PERTURBATION TECHNIQUES RAYLEIGH–SCHR¨ODINGER PERTURBATION THEORY THE BRILLOUIN–WIGNER PERTURBATION THEORY COMPARISON OF RAYLEIGH–SCHR¨ODINGER AND BRILLOUIN–WIGNER PERTURBATION THEORIES THE VARIATIONAL PRINCIPLES OF QUANTUM THEORY TIME-DEPENDENT PERTURBATION THEORY TRANSITION RATE AND FERMI GOLDEN RULE SPECI?C PERTURBATIONS AND TRANSITION RATE THE NATURAL WIDTH OF A SPECTRAL LINE DECAY RATES FOR QUANTUM SYSTEMS E?ECT OF RELAXATION ON A RESONANCE ABSORPTION SPECTRUM TRANSITION PROBABILITY DUE TO RANDOM PERTURBATIONS 4 SCATTERING THEORY SCATTERING PROBLEM: GENERAL APPROACH POTENTIAL SCATTERING SCATTERING CROSS-SECTION SCATTERING THEORY AND THE TRANSITION RATE THE FORMAL SCATTERING THEORY 5 GREEN FUNCTIONS METHOD IN MATHEMATICAL PHYSICS THE GREEN FUNCTIONS AND THE DI?ERENTIAL EQUATIONS THE GREEN FUNCTION OF THE SCHR¨ODINGER EQUATION THE PROPAGATION OF A WAVE FUNCTION TIME-DEPENDENT GREEN FUNCTIONS AND QUANTUM DYNAMICS THE ENERGY-DEPENDENT GREEN FUNCTIONS THE GREEN FUNCTIONS AND THE SCATTERING PROBLEM PRINCIPLES OF LIMITING ABSORPTION AND LIMITING AMPLITUDE IN SCATTERING THEORY BIOGRAPHY OF GEORGE GREEN 6 SYMMETRY AND INVARIANCE SYMMETRY PRINCIPLES IN PHYSICS GROUPS AND SYMMETRY TRANSFORMATIONS SYMMETRY IN QUANTUM MECHANICS INVARIANCE AND CONSERVATION PROPERTIES THE PHYSICS OF TIME REVERSAL CHIRAL SYMMETRY BIOGRAPHY OF PIERRE CURIE 7 THE ANGULAR MOMENTUM AND SPIN SPACE-ROTATION INVARIANCE ANGULAR MOMENTUM OPERATOR THE SPIN MAGNETIC MOMENT EXCHANGE FORCES AND MICROSCOPIC ORIGIN OF SPIN INTERACTIONS TIME REVERSAL SYMMETRY 8 EQUILIBRIUM STATISTICAL THERMODYNAMICS STATISTICAL THERMODYNAMICS GIBBS ENSEMBLES METHOD GIBBS AND BOLTZMANN ENTROPY THE CANONICAL DISTRIBUTION AND GIBBS THEOREM ENSEMBLES IN QUANTUM-STATISTICAL MECHANICS BIOGRAPHY OF J W GIBBS 9 DYNAMICS AND STATISTICAL MECHANICS INTERRELATION OF DYNAMICS AND STATISTICAL MECHANICS EQUIPARTITION OF ENERGY NONLINEAR OSCILLATIONS AND TIME AVERAGING 10 THERMODYNAMIC LIMIT IN STATISTICAL MECHANICS THERMODYNAMIC LIMIT IN STATISTICAL PHYSICS EQUIVALENCE AND NONEQUIVALENCE OF ENSEMBLES PHASE TRANSITIONS SMALL AND NON-STANDARD SYSTEMS CONCLUDING REMARKS 11 MAXIMUM ENTROPY PRINCIPLE MAXIMUM ENTROPY PRINCIPLE APPLICABILITY OF THE MAXIMUM ENTROPY ALGORITHM BIOGRAPHY OF E T JAYNES 12 BAND THEORY AND ELECTRONIC PROPERTIES OF SOLIDS SOLID STATE: METALS AND NONMETALS ENERGY BAND STRUCTURE OF METALS AND NONMETALS FERMI SURFACE ATOMIC ORBITALS AND TIGHT-BINDING APPROXIMATION 12 4 1 LOCALIZED ATOMIC AND MOLECULAR ORBITALS 12 4 2 TIGHT-BINDING APPROXIMATION E?ECTIVE ELECTRON MASS BIOGRAPHY OF FELIX BLOCH 13 MAGNETIC PROPERTIES OF SUBSTANCES AND MATERIALS SOLID-STATE PHYSICS OF COMPLEX MATERIALS PHYSICS OF MAGNETISM QUANTUM THEORY OF MAGNETISM LOCALIZED MODELS OF MAGNETISM 13 4 1 ISING MODEL 13 4 2 HEISENBERG MODEL PROBLEM OF MAGNETISM OF ITINERANT ELECTRONS BIOGRAPHY OF PIERRE-ERNEST WEISS 14 STATISTICAL PHYSICS OF MANY-PARTICLE SYSTEMS THEORY OF MANY-PARTICLE SYSTEMS WITH INTERACTIONS THE METHOD OF SECOND QUANTIZATION CHEMICAL POTENTIAL OF MANY-PARTICLE SYSTEMS MODEL OF DILUTE BOSE GAS BOGOLIUBOV CANONICAL TRANSFORMATION METHOD MODEL DESCRIPTION OF COMPLEX MATERIALS ITINERANT ELECTRON MODELS INTERACTING ELECTRONS ON A LATTICE AND THE HUBBARD MODEL THE ANDERSON MODEL MULTI-BAND MODELS MODEL WITH S–D HYBRIDIZATION THE S–D EXCHANGE MODEL AND THE ZENER MODEL FALICOV–KIMBALL MODEL MODEL OF DISORDERED BINARY SUBSTITUTIONAL ALLOYS THE ADEQUACY OF THE MODEL DESCRIPTION 15 THERMODYNAMIC GREEN FUNCTIONS METHODS OF THE QUANTUM FIELD THEORY AND MANY-PARTICLE SYSTEMS VARIETY OF THE GREEN FUNCTIONS TEMPERATURE GREEN FUNCTIONS TWO-TIME TEMPERATURE GREEN FUNCTIONS GREEN FUNCTIONS AND TIME CORRELATION FUNCTIONS QUASIPARTICLE MANY-BODY DYNAMICS THE METHOD OF IRREDUCIBLE GREEN FUNCTIONS GREEN FUNCTIONS AND MOMENTS OF SPECTRAL DENSITY PROJECTION METHODS AND THE IRREDUCIBLE GREEN FUNCTIONS BIOGRAPHY OF J SCHWINGER 16 APPLICATIONS OF THE GREEN FUNCTIONS METHOD PERFECT QUANTUM GASES GREEN FUNCTIONS AND PERTURBATION THEORY NATURAL WIDTH OF A SPECTRAL LINE AND GREEN FUNCTIONS SCATTERING OF NEUTRONS BY CONDENSED MATTER 16 5 1 THE TRANSITION RATE 16 5 2 TRANSITION AMPLITUDE AND CROSS-SECTION 16 5 3 SCATTERING FUNCTION AND CROSS-SECTION BIOGRAPHY OF DIRK TER HAAR 17 SPIN SYSTEMS AND THE GREEN FUNCTIONS METHOD SPIN SYSTEMS ON A LATTICE HEISENBERG ANTIFERROMAGNET GREEN FUNCTIONS AND ISOTROPIC HEISENBERG MODEL HEISENBERG FERROMAGNET AND BOSON REPRESENTATION TYABLIKOV AND CALLEN DECOUPLING ROTATIONAL INVARIANCE AND HEISENBERG MODEL HEISENBERG MODEL OF SPIN SYSTEM WITH TWO SPINS PER SITE SPIN-WAVE SCATTERING E?ECTS IN HEISENBERG FERROMAGNET HEISENBERG ANTIFERROMAGNET AT FINITE TEMPERATURES 17 9 1 HAMILTONIAN OF THE MODEL 17 9 2 QUASIPARTICLE MANY-BODY DYNAMICS OF HEISENBERG ANTIFERROMAGNET 17 9 3 GMF GREEN FUNCTION 17 9 4 DAMPING OF QUASIPARTICLE EXCITATIONS CONCLUSIONS BIOGRAPHY OF S V TYABLIKOV 18 CORRELATED FERMION SYSTEMS ON A LATTICE: HUBBARD MODEL QUASIPARTICLE MANY-BODY DYNAMICS OF LATTICE FERMION MODELS HUBBARD MODEL: WEAK CORRELATION HUBBARD MODEL: STRONG CORRELATION CORRELATIONS IN RANDOM HUBBARD MODEL INTERPOLATION SOLUTIONS OF CORRELATED MODELS E?ECTIVE PERTURBATION EXPANSION FOR THE SELF-ENERGY OPERATOR BIOGRAPHY OF JOHN HUBBARD 19 CORRELATED FERMION SYSTEMS ON A LATTICE ANDERSON MODEL HAMILTONIAN OF THE MODELS 19 2 1 SINGLE-IMPURITY ANDERSON MODEL 19 2 2 PERIODIC ANDERSON MODEL 19 2 3 TWO-IMPURITY ANDERSON MODEL THE IRREDUCIBLE GREEN FUNCTIONS METHOD AND SIAM SIAM: STRONG CORRELATION IGF METHOD AND INTERPOLATION SOLUTION OF SIAM QUASIPARTICLE DYNAMICS OF SIAM COMPLEX EXPANSION FOR A PROPAGATOR THE IMPROVED INTERPOLATIVE TREATMENT OF SIAM QUASIPARTICLE MANY-BODY DYNAMICS OF PAM QUASIPARTICLE MANY-BODY DYNAMICS OF TIAM 20 SPIN–FERMION MODEL OF MAGNETISM: QUASIPARTICLE MANY-BODY DYNAMICS THE SPIN-FERMION MODEL QUASIPARTICLE DYNAMICS OF THE (SP–D) MODEL SPIN DYNAMICS OF THE SP–D MODEL: SCATTERING REGIME GENERALIZED MEAN-FIELD GREEN FUNCTION UNCOUPLED SUBSYSTEMS COUPLED SUBSYSTEMS E?ECTS OF DISORDER IN DILUTED MAGNETIC SEMICONDUCTORS DISCUSSION 21 SPIN–FERMION MODEL OF MAGNETISM: THEORY OF MAGNETIC POLARON CHARGE AND SPIN DEGREES OF FREEDOM CHARGE DYNAMICS OF THE S–D MODEL: SCATTERING REGIME CHARGE DYNAMICS OF THE S–D MODEL: BOUND STATE REGIME MAGNETIC POLARON IN GMF DAMPING OF THE MAGNETIC POLARON STATE 22 QUANTUM PROTECTORATE AND MICROSCOPIC MODELS OF MAGNETISM MAGNETIC DEGREES OF FREEDOM MICROSCOPIC PICTURE OF MAGNETISM IN MATERIALS 22 3 1 HEISENBERG MODEL 22 3 2 ITINERANT ELECTRON MODEL 22 3 3 HUBBARD MODEL 22 3 4 MULTI-BAND MODEL: MODEL WITH S–D HYBRIDIZATION 22 3 5 SPIN–FERMION MODEL SYMMETRY AND PHYSICS OF MAGNETISM SPIN QUASIPARTICLE DYNAMICS 22 5 1 SPIN DYNAMICS OF THE HUBBARD MODEL 22 5 2 SPIN DYNAMICS OF THE SFM 22 5 3 SPIN DYNAMICS OF THE MULTI-BAND MODEL QUASIPARTICLE EXCITATION SPECTRA AND NEUTRON SCATTERING 23 QUASIAVERAGES AND SYMMETRY BREAKING GAUGE INVARIANCE SPONTANEOUS SYMMETRY BREAKING GOLDSTONE THEOREM HIGGS PHENOMENON BOGOLIUBOV QUASIAVERAGES IN STATISTICAL MECHANICS 23 6 1 BOGOLIUBOV THEOREM ON THE SINGULARITY OF 1/Q2 23 6 2 BOGOLIUBOV’S INEQUALITY AND THE MERMIN–WAGNER THEOREM BROKEN SYMMETRIES AND CONDENSED MATTER PHYSICS 23 7 1 SUPERCONDUCTIVITY 23 7 2 ANTIFERROMAGNETISM 23 7 3 BOSE SYSTEMS CONCLUSIONS AND DISCUSSIONS BIOGRAPHY OF N N BOGOLIUBOV 24 EMERGENCE AND EMERGENT PHENOMENA EMERGENCE CONCEPT EMERGENT PHENOMENA QUANTUM MECHANICS AND ITS EMERGENT MACROPHYSICS EMERGENT PHENOMENA IN QUANTUM CONDENSED MATTER PHYSICS 25 ELECTRON–LATTICE INTERACTION IN METALS AND ALLOYS ELECTRON-LATTICE INTERACTION IN CONDENSED MATTER SYSTEMS MODI?ED TIGHT-BINDING APPROXIMATION 25 3 1 ELECTRON GREEN FUNCTION 25 3 2 PHONON GREEN FUNCTION 25 3 3 RENORMALIZATION OF THE ELECTRON AND PHONON SPECTRA RENORMALIZED SPECTRUM OF THE MOTT–HUBBARD INSULATOR THE ELECTRON–PHONON SPECTRAL FUNCTION ELECTRON–LATTICE INTERACTION IN DISORDERED BINARY ALLOYS 25 6 1 THE MODEL 25 6 2 ELECTRON GREEN FUNCTIONS FOR ALLOY 25 6 3 GREEN FUNCTION FOR LATTICE VIBRATIONS IN ALLOY 25 6 4 THE CON?GURATIONAL AVERAGING 25 6 5 THE ELECTRONIC SPECI?C HEAT BIOGRAPHY OF HERBERT FR¨OHLICH 26 SUPERCONDUCTIVITY IN TRANSITION METALS AND THEIR DISORDERED ALLOYS THE MICROSCOPIC THEORY OF SUPERCONDUCTIVITY 26 2 1 THE NAMBU FORMALISM 26 2 2 THE ELIASHBERG EQUATIONS EQUATIONS OF SUPERCONDUCTIVITY IN WANNIER REPRESENTATIONS STRONG-COUPLING EQUATIONS OF SUPERCONDUCTIVITY EQUATIONS OF SUPERCONDUCTIVITY IN DISORDERED BINARY ALLOYS 26 5 1 THE MODEL HAMILTONIAN 26 5 2 ELECTRON GREEN FUNCTION AND MASS OPERATOR 26 5 3 RENORMALIZED LATTICE GREEN FUNCTION 26 5 4 CON?GURATIONAL AVERAGING 26 5 5 SIMPLEST METHOD OF AVERAGING 26 5 6 GENERAL AVERAGING SCHEME 26 5 7 THE RANDOM CONTACT MODEL 26 5 8 CPA EQUATIONS FOR SUPERCONDUCTIVITY IN THE CONTACT MODEL 26 5 9 LINEARIZED EQUATIONS AND TRANSITION TEMPERATURE THE PHYSICS OF LAYERED SYSTEMS AND SUPERCONDUCTIVITY 26 6 1 LAYERED CUPRATES 26 6 2 CRYSTAL STRUCTURE OF CUPRATES AND MERCUROCUPRATES 26 6 3 THE LAWRENCE–DONIACH MODEL 27 SPECTRAL PROPERTIES OF THE GENERALIZED SPIN-FERMION MODELS GENERALIZED SFM SPIN DYNAMICS OF THE D–F MODEL 27 3 1 GENERALIZED MEAN-?ELD GREEN FUNCTION 27 3 2 DYSON EQUATION FOR D–F MODEL SELF-ENERGY AND DAMPING CHARGE DYNAMICS OF THE D–F MODEL 28 CORRELATION E?ECTS IN HIGH-TC SUPERCONDUCTORS AND HEAVY FERMION COMPOUNDS THE ELECTRONIC PROPERTIES OF CORRELATED SYSTEMS THE MODEL HAMILTONIAN THE E?ECTIVE HAMILTONIANS COEXISTENCE OF SPIN AND CARRIER SUBSYSTEMS COMPETITION OF INTERACTIONS IN KONDO SYSTEMS DYNAMICS OF CARRIERS IN THE SPIN–FERMION MODEL 28 7 1 HOLE DYNAMICS IN CUPRATES 28 7 2 HUBBARD MODEL AND T–J MODEL 28 7 3 HOLE SPECTRUM OF T–J MODEL 28 7 4 THE KONDO–HEISENBERG MODEL 28 7 5 HOLE DYNAMICS IN THE KONDO–HEISENBERG MODEL 28 7 6 DYNAMICS OF SPIN SUBSYSTEM 28 7 7 DAMPING OF HOLE QUASIPARTICLES 29 GENERALIZED MEAN FIELDS AND VARIATIONAL PRINCIPLE OF BOGOLIUBOV THE HELMHOLTZ FREE ENERGY APPROXIMATE CALCULATIONS OF THE HELMHOLTZ FREE ENERGY THE MEAN FIELD CONCEPT THE MATHEMATICAL TOOLS VARIATIONAL PRINCIPLE OF BOGOLIUBOV APPLICATIONS OF THE BOGOLIUBOV VARIATIONAL PRINCIPLE THE VARIATIONAL SCHEMES AND BOUNDS ON FREE ENERGY THE HARTREE–FOCK–BOGOLIUBOV MEAN FIELDS METHOD OF AN APPROXIMATING HAMILTONIAN 30 NONEQUILIBRIUM STATISTICAL THERMODYNAMICS ENSEMBLE METHOD IN THE THEORY OF IRREVERSIBILITY STATISTICAL MECHANICS OF IRREVERSIBILITY BOLTZMANN EQUATION THE METHOD OF TIME CORRELATION FUNCTIONS KUBO LINEAR RESPONSE THEORY FLUCTUATION THEOREM AND GREEN–KUBO RELATIONS CONDITIONS FOR LOCAL EQUILIBRIUM MODI?ED PROJECTION METHODS 31 METHOD OF THE NONEQUILIBRIUM STATISTICAL OPERATOR NONEQUILIBRIUM ENSEMBLES THE NSO METHOD THE RELEVANT OPERATORS CONSTRUCTION OF THE NSO 32 NONEQUILIBRIUM STATISTICAL OPERATOR AND TRANSPORT EQUATIONS HYDRODYNAMIC EQUATIONS THE TRANSPORT AND KINETIC EQUATIONS SYSTEM IN THERMAL BATH: GENERALIZED KINETIC EQUATIONS SYSTEM IN THERMAL BATH: RATE AND MASTER EQUATIONS A DYNAMICAL SYSTEM IN A THERMAL BATH SCHR¨ODINGER-TYPE EQUATION WITH DAMPING FOR A DYNAMICAL SYSTEM IN A THERMAL BATH 33 APPLICATIONS OF THE NONEQUILIBRIUM STATISTICAL OPERATOR DAMPING E?ECTS IN A SYSTEM INTERACTING WITH A THERMAL BATH THE NATURAL WIDTH OF SPECTRAL LINE OF THE ATOMIC SYSTEM EVOLUTION OF A SYSTEM IN AN ALTERNATING EXTERNAL FIELD STATISTICAL THEORY OF SPIN RELAXATION AND DI?USION IN SOLIDS 33 4 1 DYNAMICS OF NUCLEAR SPIN SYSTEM 33 4 2 NUCLEAR SPIN–LATTICE RELAXATION 33 4 3 SPIN DI?USION OF NUCLEAR MAGNETIC MOMENT 33 4 4 SPIN DI?USION COE?CIENT 33 4 5 STOCHASTICITY OF SPIN SUBSYSTEM 33 4 6 SPIN DI?USION COE?CIENT IN DILUTE ALLOYS OTHER APPLICATIONS OF THE NSO METHOD 34 GENERALIZED VAN HOVE FORMULA FOR SCATTERING OF PARTICLES BY STATISTICAL MEDIUM DENSITY CORRELATION FUNCTION SCATTERING FUNCTION AND CROSS-SECTION THE VAN HOVE FORMULA VAN HOVE FORMALISM FOR THE NONEQUILIBRIUM STATISTICAL MEDIUM SCATTERING OF BEAM OF PARTICLES BY THE NONEQUILIBRIUM MEDIUM BIOGRAPHY OF LEON VAN HOVE 35 ELECTRONIC TRANSPORT IN METALLIC SYSTEMS MANY-PARTICLE INTERACTING SYSTEMS AND CURRENT OPERATOR CURRENT OPERATOR FOR THE TIGHT-BINDING ELECTRONS CHARGE AND HEAT TRANSPORT 35 4 1 ELECTRICAL RESISTIVITY AND OHM’S LAW 35 4 2 DRUDE–LORENTZ MODEL THE TEMPERATURE DEPENDENCE OF CONDUCTIVITY CONDUCTIVITY OF ALLOYS MAGNETORESISTANCE AND THE HALL E?ECT THERMAL CONDUCTION IN SOLIDS LINEAR MACROSCOPIC TRANSPORT EQUATIONS STATISTICAL MECHANICS AND TRANSPORT COE?CIENTS TRANSPORT THEORY AND ELECTRICAL CONDUCTIVITY METHOD OF TIME CORRELATION FUNCTIONS AND LINEAR RESPONSE THEORY GREEN FUNCTIONS IN THE THEORY OF IRREVERSIBLE PROCESSES THE ELECTRICAL CONDUCTIVITY TENSOR LINEAR RESPONSE THEORY: PRO ET CONTRA GENERALIZED KINETIC EQUATIONS ELECTRICAL CONDUCTIVITY RESISTIVITY OF TRANSITION METAL WITH NONSPHERICAL FERMI SURFACE TEMPERATURE DEPENDENCE OF RESISTIVITY EQUIVALENCE OF NSO APPROACH AND KUBO FORMALISM HIGH-TEMPERATURE RESISTIVITY AND MTBA RESISTIVITY OF DISORDERED ALLOYS BIOGRAPHY OF GEORG SIMON OHM