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Statistical Mechanics

From First Principles to Macroscopic Phenomena

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Hardcover | 19 February 2007

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296 Pages

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24.41 x 16.99 x 1.75

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Based on the author's graduate course taught over many years in several physics departments, this 2006 book takes a 'reductionist' view of statistical mechanics, while describing the main ideas and methods underlying its applications. It implicitly assumes that the physics of complex systems as observed is connected to fundamental physical laws represented at the molecular level by Newtonian mechanics or quantum mechanics. Organised into three parts, the first section describes the fundamental principles of equilibrium statistical mechanics. The next section describes applications to phases of increasing density and order: gases, liquids and solids; it also treats phase transitions. The final section deals with dynamics, including a careful account of hydrodynamic theories and linear response theory. This textbook is suitable for a one year graduate course in statistical mechanics for physicists, chemists and chemical engineers. Problems are included following each chapter, with solutions to selected problems provided.

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Preface	p. ix
Introduction	p. 1
Foundations of equilibrium statistical mechanics	p. 5
The classical distribution function	p. 7
Foundations of equilibrium statistical mechanics	p. 7
Liouville's theorem	p. 14
The distribution function depends only on additive constants of the motion	p. 16
Microcanonical distribution	p. 20
References	p. 24
Problems	p. 24
Quantum mechanical density matrix	p. 27
Microcanonical density matrix	p. 33
Reference	p. 34
Problems	p. 34
Thermodynamics	p. 37
Definition of entropy	p. 37
Thermodynamic potentials	p. 38
Some thermodynamic relations and techniques	p. 42
Constraints on thermodynamic quantities	p. 46
References	p. 49
Problems	p. 49
Semiclassical limit	p. 51
General formulation	p. 51
The perfect gas	p. 52
Problems	p. 56
States of matter in equilibrium statistical physics	p. 57
Perfect gases	p. 59
Classical perfect gas	p. 60
Molecular ideal gas	p. 62
Quantum perfect gases: general features	p. 69
Quantum perfect gases: details for special cases	p. 71
Perfect Bose gas at low temperatures	p. 74
Perfect Fermi gas at low temperatures	p. 78
References	p. 81
Problems	p. 81
Imperfect gases	p. 85
Method I for the classical virial expansion	p. 86
Method II for the virial expansion: irreducible linked clusters	p. 95
Application of cumulants to the expansion of the free energy	p. 102
Cluster expansion for a quantum imperfect gas (extension of method I)	p. 108
Gross-Pitaevskii-Bogoliubov theory of the low temperature weakly interacting Bose gas	p. 115
References	p. 122
Problems	p. 122
Statistical mechanics of liquids	p. 125
Definitions of n-particle distribution functions	p. 126
Determination of g(r) by neutron and x-ray scattering	p. 128
BBGKY hierarchy	p. 133
Approximate closed form equations for g(r)	p. 135
Molecular dynamics evaluation of liquid properties	p. 136
References	p. 143
Problems	p. 144
Quantum liquids and solids	p. 145
Fundamental postulates of Fermi liquid theory	p. 146
Models of magnets	p. 150
Physical basis for models of magnetic insulators: exchange	p. 150
Comparison of Ising and liquid-gas systems	p. 153
Exact solution of the paramagnetic problem	p. 153
High temperature series for the Ising model	p. 154
Transfer matrix	p. 157
Monte Carlo methods	p. 158
References	p. 159
Problems	p. 160
Phase transitions: static properties	p. 161
Thermodynamic considerations	p. 161
Critical points	p. 166
Phenomenology of critical point singularities: scaling	p. 167
Mean field theory	p. 172
Renormalization group: general scheme	p. 177
Renormalization group: the Landau-Ginzburg model	p. 181
References	p. 189
Problems	p. 189
Dynamics	p. 193
Hydrodynamics and definition of transport coefficients	p. 195
General discussion	p. 195
Hydrodynamic equations for a classical fluid	p. 196
Fluctuation-dissipation relations for hydrodynamic transport coefficients	p. 199
References	p. 214
Problems	p. 214
Stochastic models and dynamical critical phenomena	p. 217
General discussion of stochastic models	p. 217
Generalized Langevin equation	p. 217
General discussion of dynamical critical phenomena	p. 221
References	p. 242
Problems	p. 242
Solutions to selected problems	p. 243
Index	p. 281
Table of Contents provided by Ingram. All Rights Reserved.

Statistical Mechanics

From First Principles to Macroscopic Phenomena

At a Glance

Hardcover

Shipping

How to return your order

Defective items

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