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Essential Statistical Physics [Hardback]

3.50/5 (4 ratings by Goodreads)
(Simon Fraser University, British Columbia)
  • Formāts: Hardback, 260 pages, height x width x depth: 252x193x16 mm, weight: 720 g, Worked examples or Exercises; 7 Halftones, black and white; 71 Line drawings, black and white
  • Izdošanas datums: 16-Jul-2020
  • Izdevniecība: Cambridge University Press
  • ISBN-10: 1108480780
  • ISBN-13: 9781108480789
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Essential Statistical PhysicsPalielināt
  • Formāts: Hardback, 260 pages, height x width x depth: 252x193x16 mm, weight: 720 g, Worked examples or Exercises; 7 Halftones, black and white; 71 Line drawings, black and white
  • Izdošanas datums: 16-Jul-2020
  • Izdevniecība: Cambridge University Press
  • ISBN-10: 1108480780
  • ISBN-13: 9781108480789
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9781108480789.html
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"This clear and pedagogical text delivers a concise overview of classical and quantum statistical physics. Essential Statistical Physics shows students how to relate the macroscopic properties of physical systems to their microscopic degrees of freedom, preparing them for graduate courses in areas such as biophysics, condensed matter physics, atomic physics and statistical mechanics. Topics covered include the microcanonical, canonical, and grand canonical ensembles, Liouville's theorem, kinetic theory, non-interacting Fermi and Bose systems and phase transitions, and the Ising model. Detailed steps are given in mathematical derivations, allowing students to quickly develop a deep understanding of statistical techniques. End-of-chapter problems reinforcekey concepts and introduce more advanced applications, and appendices provide a detailed review of thermodynamics and related mathematical results. This succinct book offers a fresh and intuitive approach to one of the most challenging topics in the corephysics curriculum, and provides students with a solid foundation for tackling advanced topics in statistical mechanics"--

Recenzijas

'At last a textbook that contains all the required elements for a modern advanced undergraduate course on statistical physics: foundations, quantum statistical mechanics, phase transitions and dynamics. I particularly like the derivation of ensembles through maximization of Gibbs entropy and the Langevin description of Brownian motion. Plenty of instructive problems within ten digestible chapters make this a text I can recommend to my students.' Martin Evans, University of Edinburgh 'Statistical mechanics is a vast and fascinating topic, sometimes intimidating beginning students. Kennett succeeds in delivering an agile, fresh and modern exposition of the essential ideas and methods, in addition to a well-thought selection of examples and applications borrowed from all branches of physics. Students and teachers alike will enjoy the carefully organized table of contents for self-study and lecture preparation.' Roberto Raimondi, Roma Tre University 'This book incorporates, into a single course, ideas and theoretical techniques in statistical physics and quantum mechanics that are connected by the physical phenomena they are meant to describe. Yet they are rarely all found in the same text. Professor Kennett offers students of theoretical physics a rare opportunity to acquire a mature understanding of their impact and meaning.' Herbert Fertig, Indiana University, Bloomington

Papildus informācija

Delivers a clear and concise exposition of key topics in statistical physics, accompanied by detailed derivations and practice problems.
Preface xi
1 Introduction
1(24)
1.1 What is Statistical Mechanics?
1(1)
1.2 Probabilistic Behaviour
2(14)
1.2.1 Axioms of Probability
3(1)
1.2.2 Example: Coin Toss Experiment
4(1)
1.2.3 Probability Distributions
5(2)
1.2.4 Example: Random Walk
7(4)
1.2.5 Large-Af Limit of the Binomial Distribution
11(4)
1.2.6 Central Limit Theorem
15(1)
1.3 Microstates and Macrostates
16(3)
1.3.1 Example: Non-interacting Spins in a Solid
17(2)
1.4 Information, Ignorance and Entropy
19(2)
1.5 Summary
21(1)
Problems
21(4)
2 The Microcanonical Ensemble
25(16)
2.1 Thermal Contact
26(5)
2.1.1 Heat Flow in the Approach to Equilibrium
28(1)
2.1.2 Principle of Maximum Entropy
29(1)
2.1.3 Energy Resolution and Entropy
30(1)
2.2 Gibbs Entropy
31(1)
2.3 Shannon Entropy
32(2)
2.4 Example: Non-interacting Spins in a Solid
34(2)
2.5 Summary
36(1)
Problems
37(4)
3 Liouville's Theorem
41(7)
3.1 Phase Space and Hamiltonian Dynamics
41(4)
3.2 Ergodic Hypothesis
45(1)
3.2.1 Non-ergodic Systems
46(1)
3.3 Summary
46(1)
Problems
46(2)
4 The Canonical Ensemble
48(38)
4.1 Partition Function
48(2)
4.2 Bridge Equation in the Canonical Ensemble
50(5)
4.2.1 Boltzmann Distribution
52(1)
4.2.2 Derivatives of the Partition Function
52(2)
4.2.3 Equivalence of the Canonical and Microcanonical Ensembles
54(1)
4.3 Connections to Thermodynamics
55(1)
4.4 Examples
56(9)
4.4.1 Two-Level System
56(3)
4.4.2 Quantum Simple Harmonic Oscillator
59(2)
4.4.3 Classical Partition Function and Classical Harmonic Oscillator
61(1)
4.4.4 Rigid Rotor
62(2)
4.4.5 Particle in a Box
64(1)
4.5 Ideal Gas
65(10)
4.5.1 Uncoupled Subsystems
65(2)
4.5.2 Distinguishable and Indistinguishable Particles
67(3)
4.5.3 Ideal Gas
70(3)
4.5.4 Example: Entropy of Mixing
73(2)
4.6 Non-ideal Gases
75(3)
4.7 The Equipartition Theorem
78(2)
4.7.1 Example: The Ideal Gas
79(1)
4.7.2 Dulong and Petit Law
79(1)
4.8 Summary
80(1)
Problems
81(5)
5 Kinetic Theory
86(21)
5.1 Maxwell-Boltzmann Velocity Distribution
86(3)
5.1.1 Density of States
87(1)
5.1.2 Maxwell-Boltzmann Velocity Distribution
87(2)
5.2 Properties of the Maxwell-Boltzmann Velocity Distribution
89(2)
5.2.1 Distribution of Speeds
90(1)
5.3 Kinetic Theory for an Ideal Gas
91(4)
5.3.1 Pressure in an Ideal Gas
92(2)
5.3.2 Effusion
94(1)
5.4 Brownian Motion
95(3)
5.5 Diffusion
98(4)
5.5.1 Mean Free Path and Collision Time
98(2)
5.5.2 Fick's Law
100(2)
5.6 Transport
102(1)
5.7 Summary
103(1)
Problems
104(3)
6 The Grand Canonical Ensemble
107(18)
6.1 Chemical Potential
107(4)
6.1.1 Example: Ideal Gas
109(2)
6.2 Grand Canonical Partition Function
111(4)
6.2.1 Bridge Equation
112(2)
6.2.2 Derivatives of the Grand Potential
114(1)
6.3 Examples
115(3)
6.3.1 Fermions in a Two-Level System
115(2)
6.3.2 The Langmuir Adsorption Isotherm
117(1)
6.4 Chemical Equilibrium and the Law of Mass Action
118(3)
6.4.1 The Law of Mass Action
119(2)
6.5 Summary
121(1)
Problems
122(3)
7 Quantum Statistical Mechanics
125(14)
7.1 Quantum Statistics
125(2)
7.2 Distinguishable Particles and Maxwell-Boltzmann Statistics
127(2)
7.2.1 Maxwell-Boltzmann Statistics
128(1)
7.3 Quantum Particles in the Grand Canonical Ensemble
129(4)
7.3.1 Fermi-Dirac Distribution
131(1)
7.3.2 Bose-Einstein Distribution
132(1)
7.4 Density of States and Thermal Averages
133(3)
7.4.1 Thermal Averages Using the Density of States
135(1)
7.5 Summary
136(1)
Problems
137(2)
8 Fermions
139(22)
8.1 Chemical Potential for Fermions
139(5)
8.1.1 Zero Temperature: The Fermi Energy
139(1)
8.1.2 Non-zero Temperature: Sommerfeld Expansion
140(3)
8.1.3 Temperature Dependence of the Chemical Potential
143(1)
8.2 Thermodynamic Properties of a Fermi Gas
144(4)
8.2.1 Energy and Heat Capacity
144(1)
8.2.2 Pressure of a Fermi Gas
145(1)
8.2.3 Entropy of a Fermi Gas
146(1)
8.2.4 Number Fluctuations
147(1)
8.2.5 Another View of Temperature Dependence of Thermodynamic Properties
148(1)
8.3 Applications
148(9)
8.3.1 Metals and the Fermi Sea
148(3)
8.3.2 White Dwarf Stars
151(6)
8.3.3 Neutron Stars
157(1)
8.4 Summary
157(1)
Problems
157(4)
9 Bosons
161(29)
9.1 Photons and Blackbody Radiation
161(9)
9.1.1 Blackbody Radiation
162(1)
9.1.2 Density of States
162(1)
9.1.3 Number Density
163(1)
9.1.4 Energy Density
164(3)
9.1.5 Example: Cosmic Microwave Background Radiation
167(1)
9.1.6 Radiation Pressure
168(1)
9.1.7 Stefan-Boltzmann Law
169(1)
9.2 Bose-Einstein Condensation
170(6)
9.2.1 Superfluidity
174(2)
9.3 Low-Temperature Properties of a Bose Gas
176(4)
9.3.1 Chemical Potential
176(1)
9.3.2 Internal Energy and Heat Capacity
177(3)
9.4 Bosonic Excitations: Phonons and Magnons
180(5)
9.4.1 Phonons
180(1)
9.4.2 The Debye Model
181(3)
9.4.3 Magnons
184(1)
9.5 Summary
185(1)
Problems
186(4)
10 Phase Transitions and Order
190(32)
10.1 Introduction to the Ising Model
190(3)
10.2 Solution of the Ising Model
193(9)
10.2.1 Order Parameters and Broken Symmetry
193(1)
10.2.2 General Strategy for Solution of the Ising Model
194(1)
10.2.3 Mean Field Theory
195(7)
10.3 Role of Dimensionality
202(3)
10.3.1 One Dimension
202(1)
10.3.2 Two Dimensions
203(2)
10.4 Exact Solutions of the Ising Model
205(4)
10.4.1 Exact Solution in One Dimension
205(3)
10.4.2 Exact Solution in Two Dimensions
208(1)
10.5 Monte Carlo Simulation of the Ising Model
209(3)
10.5.1 Importance Sampling
209(1)
10.5.2 Metropolis Algorithm
210(1)
10.5.3 Initial Conditions and Equilibration
210(2)
10.6 Connection between the Ising Model and the Liquid-Gas Transition
212(1)
10.7 Landau Theory
213(3)
10.7.1 Symmetry-Breaking Fields
214(2)
10.7.2 Landau Theory and First-Order Phase Transitions
216(1)
10.8 Summary
216(1)
Problems
217(5)
Appendix A Gaussian Integrals and Stirling's Formula
222(5)
A.1 Gaussian Integrals
222(1)
A.2 Gamma Function
223(1)
A.3 Stirling's Formula
224(3)
Appendix B Primer on Thermal Physics
227(12)
B.1 Thermodynamic Equilibrium
227(4)
B.1.1 Reversible and Irreversible Processes
227(1)
B.1.2 State Functions
228(2)
B.1.3 Work and Heat
230(1)
B.2 The Laws of Thermodynamics
231(2)
B.3 Thermodynamic Potentials
233(3)
B.3.1 Legendre Transforms and Free Energies
235(1)
B.4 Maxwell Relations
236(3)
B.4.1 Useful Partial Derivative Relations
237(1)
B.4.2 Example: Relationship between Cy and Cp
238(1)
Appendix C Heat Capacity Cusp in Bose Systems
239(4)
C.1 Heat Capacity
241(2)
References 243(1)
Index 244
Malcolm P. Kennett is Associate Professor at Simon Fraser University, Canada. He studied at the University of Sydney and Princeton University and was a postdoctoral fellow at the University of Cambridge. He has taught statistical mechanics at both undergraduate and graduate level for many years and has been recognized for the high quality of his teaching and innovative approaches to the undergraduate and graduate curriculum. His research is focused on condensed matter theory and he has made contributions to the theory of spin glasses, dilute magnetic semiconductors, out of equilibrium dynamics in ultracold atoms, and the Quantum Hall effect in graphene.