DeutschesFachbuch.de : Statistical Physics Von Tony Guénault

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Table of contents
Preface ix
1 Basic ideas 1
1.1 The macrostate 1
1.2 Microstates 2
1.3 The averaging postulate 3
1.4 Distributions 4
1.5 The statistical method in outline 6
1.6 A model example 7
1.7 Statistical entropy and microstates 10
1.8 Summary 11
2 Distinguishable particles 13
2.1 The Thermal Equilibrium Distribution 14
2.2 What are α and β 17
2.3 A statistical definition of temperature 18
2.4 The boltzmann distribution and the partition function 21
2.5 Calculation of thermodynamic functions 22
2.6 Summary 23
3 Two examples 25
3.1 A Spinsolid 25
3.2 Localized harmonic oscillators 36
3.3 Summary 40
4 Gases: the density of states 43
4.1 Fitting waves into boxes 43
4.2 Other information for statistical physics 47
4.3 An example - helium gas 48
4.4 Summary 49
5 Gases: the distributions 51
5.1 Distribution in groups 51
5.2 Identical particles - fermions and bosons 53
5.3 Counting microstates for gases 55
5.4 The three distributions 58
5.5 Summary 61
6 Maxwell-Boltzmann gases 63
6.1 The validity of the Maxwell-Boltzmann limit 63
6.2 The Maxwell-Boltzmann distribution of speeds 65
6.3 The connection to thermodynamics 68
6.4 Summary 71
7 Diatomic gases 73
7.1 Energy contributions in diatomic gases 73
7.2 Heat capacity of a diatomic gas 75
7.3 The heat capacity of hydrogen 78
7.4 Summary 81
8 Fermi-Dirac gases 83
8.1 Properties of an ideal Fermi-Dirac gas 84
8.2 Application to metals 91
8.3 Application to helium-3 92
8.4 Summary 95
9 Bose-Einstein gases 97
9.1 Properties of an ideal Bose-Einstein gas 97
9.2 Application to helium-4 101
9.3 Phoney bosons 104
9.4 A note about cold atoms 109
9.5 Summary 109
10 Entropy in other situations 111
10.1 Entropy and disorder 111
10.2 An assembly at fixed temperature 114
10.3 Vacancies in solids 116
11 Phase transitions 119
11.1 Types of phase transition 119
11.2 Ferromagnetism of a spinsolid 120
11.3 Real ferromagnetic materials 126
11.4 Order-disorder transformations in alloys 127
12 Two new ideas 129
12.1 Statics or dynamics? 129
12.2 Ensembles - a larger view 132
13 Chemical thermodynamics 137
13.1 Chemical potential revisited 137
13.2 The grand canonical ensemble 139
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Index
AActivation energy 151, 152
Adiabatic demagnetization 30-4, 32
Averaging postulate 3-4
B β and temperature 18-9, 61
Beta-brass 127-8, 197
Big bang 175-6
Blackbody radiation 104-7, 176
Black holes 177, 180
Boltzmann distribution 13, 16-17, 115-6, 132
Boltzmann factor 22, 117, 133, 152, 175
Bose-Einstein condensation 99-101, 109
Bose-Einstein gases 97-110
Bose-Einstein (BE) statistics 59-60, 97-9, 142-4
Bose temperature 99
Bosons 53, 56-7, 104, 129-31
CChemical equilibrium 148-9
Chemical potential 23, 137-9, 146-9
Chemical reactions 146-52, 198
Classical limit 39, 57-8, 63-5, 108, 143
Classical statistics 165-6
Clausius-Clapeyron equation 93-4, 102
CMN (cerium magnesium nitrate) 30-6
Cold atoms 109
Configuration integral 167
Cooling methods 30-4, 94, 109, 112, 163
Cooper pairs 170, 172
Counting microstates 6-8, 14, 55-8
Counting problems 181-2, 184-5
Critical exponents 127
Curie's law 34-6, 35, 125, 193
Curie temperature, Tc 122-3, 125-7
Curie-Weiss law 125-7
DDebye model of lattice vibrations 108, 108, 196
Degeneracy parameter 65, 83-4, 87, 98-9
Density of states
- basic ideas 43-8
- for BE gas 98-9
- for electrons in metals 91-2, 92
- for FD gas 85-6, 88-90
- for helium gas 48-9
- in restricted geometry 46-7
- with interactions 157, 157-8
- for photons 105
Diatomic gases 40, 73-81
Dispersion relation 48, 107-8, 156-7, 157, 159, 177-8
Distinguishable particles 13-24, 115-6
Distribution
- definition 4-6
- determination of, see Statistical method
- for gases 51-2
Distribution function 52, 58-61
- see also Bose-Einstein statistics; Fermi-Dirac statistics; Maxwell-Boltzmann statis...
EEinstein model of vibrations in a solid 40, 108
Electrons in metals 84, 91-2, 154-8
Energy scales 26, 39, 78-81
Entropy, S
- of BE gas 113-4
- of FD gas 90-1, 113-4
- of ferromagnet 124-5, 125
- of isotopes 111-2
- of MB gas 68-9, 113-4
- of oscillators 38
- of superconductor 171
- of two-state particles 28, 29
- of vacancies 116-7
Entropy expression for gases 69, 145-6
Entropy, statistical definition 10-11, 20-1, 111-4, 140
Equation of state 70-1, 77, 166-8
Equipartition of energy 39, 67, 78-9
FFermi-Dirac gases 83-95
Fermi-Dirac integrals 18 8-9
Fermi-Dirac (FD) statistics 58-9, 84-5, 85, 142-4
Fermi energy 85-8
Fermi surface 88
Fermions 53-4, 55-6, 83, 131-2
Ferromagnetism 120-7
Fitting waves into boxes
- basis 43-7
- for BE gas 98
- for FD gas 85-6
- for helium gas 48-9
- for MB gas 64, 66, 75
- for phonons 107-8
- for photons 105
Fluctuations 134, 152
Free energy (Helmholtz), F
- for assembly at fixed 7 115
- of ferromagnet 123-4, 124
- of localized particles 23
- of MB gas 70-1
- of vacancies 116-7
GGibbs free energy, G 119-20, 120, 137-9, 146-7
Gibbs paradox 71
Grand canonical ensemble 136, 139-41
- applied to ideal gases 141-6
Grand partition function 140, 142-3, 145-6
Grouped distribution 51-2, 52
HHarmonic oscillators 36-40, 76
Heat capacity, C
- of BE gas 101
- of diatomic gas 75-7, 78
- of FD gas 89, 90
- of ferromagnet 125
- of hydrogen 78-81, 79
- of MB gas 68
- of oscillators 37-8, 38
- of solids 107-8, 108
- of superconductor 171
- of two-state particles 27, 28
Helium-3 liquid 33, 92-4, 158-63, 172-4
Helium-3-helium 4 solutions 33, 112, 163
Helium-4 liquid 101-4, 163-4
Helium gas 48-9, 65
Hydrogen gas 78-81
I - dentical particles 53-4, 71, 73, 79-81
Imperfect gases 164-8
Interacting particles 103, 153-68
Intermediate statistics 194, 196
Internal energy, U
- of BE gas 101
- of FD gas 88-9, 90
- of MB gas 68
- of oscillators 37-8, 38
- of photon gas 105-6
- of two-state particles 27, 27
Ising model 121, 127
Isotopic disorder 111-2
LLagrange undetermined multipliers 16, 58-60, 115-6, 139-40
Lambda transition 102-4, 102, 103, 127, 128
Landau Fermi liquid theory 92-3, 158-61
Lasers and negative temperatures 131, 193
Localized particles 13-14, 26-41, 112-3
Longand short-range order 121, 126-7, 128
MMacrostate 1-2, 114-6, 132-3, 135, 139-40
Magnetic solids 29-36, 91-2, 120-7
Magnetization
- of spin 2 solid 34-6, 35
- of conduction electrons 91-2, 92
- of ferromagnet 120-6
Mass action, law of 149-50
Matter and radiation 129-31
Maxwell-Boltzmann gases 57-8, 60-2, 63-72
Maxwell-Boltzmann integrals 187-8
Maxwell-Boltzmann speed distribution 65-7, 67
Maxwell-Boltzmann (MB) statistics 60-2, 144-6
Mean field approximation 121, 127
Metastable states 112, 176
Microstates 2-3, 133, 139
- and entropy 10-11
Mixed systems 71, 111-2, 146-8
Modified BE distribution 104, 129-30
NNanoscience 46-7
Neutron stars 84, 176-180
Neutron-proton ratio 175-6
OOpen systems 136, 139-46
Order-disorder transformation 127-8
Order parameter 120, 121 -6, 122, 127-8
Ortho-para conversion 80-1, 195
PPartition function
- for an assembly 134-5
- definition 17, 22
- factorization in diatomic gas 73-4
- of MB gas 63-4
- of oscillator 36-7
- of reactants 149-50
- of two-state particle 25
- see also Classical statistics; Grand partition function
Pauli exclusion principle 54
- see also Fermi-Dirac statistics
Phase diagram
- helium-3 93, 173
- helium-4 102
Phase space 165-6
Phase transitions 119-28, 138-9
- in alloys 127-8
- in BE gas 99-101, 100
- classification 119-20
- in ferromagnet 120-7
- in helium-3 92-4, 93, 94, 172-4, 173
- in helium-4 101-4, 102, 103
- second order 119-25, 125
- see also Lambda transition;
- Superconductivity ;
- Superfluidity
Phonons 104, 107-8, 156-7
Photon gas 104-7, 106, 129-31
Planck radiation formula 105-7, 106
Polarization, see Spin factor
Pressure, P
- of BE gas 101
- of FD gas 90, 90, 177-8
- of MB gas 70-1
- of radiation 106-7
- of relativistic FD gas 178
Pulsars 180
QQuasiparticles 153, 158-63
RReaction rates 150-2, 176
Rotation in gases 76-7, 79-81
SSackur-Tetrode equation 69, 145-6
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