## Statistical mechanicsUnlike most other texts on the subject, this clear, concise introduction to the theory of microscopic bodies treats the modern theory of critical phenomena. Provides up-to-date coverage of recent major advances, including a self-contained description of thermodynamics and the classical kinetic theory of gases, interesting applications such as superfluids and the quantum Hall effect, several current research applications, The last three chapters are devoted to the Landau-Wilson approach to critical phenomena. Many new problems and illustrations have been added to this edition. |

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Page 76

LIOUVILLE'S THEOREM ff + I(|/"+a^)-° Proof. Since the total number of systems in

an ensemble is conserved, the number of representative points leaving any

volume in Aspace per second must be equal to the rate of decrease of the

number of representative points in the same volume. Let w be an arbitrary

volume in Aspace and let S be its surface. If we denote by v the 6Af-dimensional

LIOUVILLE'S THEOREM ff + I(|/"+a^)-° Proof. Since the total number of systems in

an ensemble is conserved, the number of representative points leaving any

volume in Aspace per second must be equal to the rate of decrease of the

number of representative points in the same volume. Let w be an arbitrary

volume in Aspace and let S be its surface. If we denote by v the 6Af-dimensional

**vector**whose components are v = (flt P» - - - □ Alv ; <}lt . . . , ?3.v) and n the**vector**locally normal to ...Page 254

Thus for given k there are two and only two independent polarization

we impose periodic boundary conditions on E(r, /) in a cube of volume V = L3, we

obtain the following allowed values of k : _ 277-n L (12-3) n = a

components are 0, ±1, ±2, . . . Thus the number of allowed momentum values

between k and k + dk is — 4nk'dk (12.4) (277)3 Photons obey Bose statistics, for

they are indistinguishable and there can be any number of photons with the

same k and ...

Thus for given k there are two and only two independent polarization

**vectors**e. Ifwe impose periodic boundary conditions on E(r, /) in a cube of volume V = L3, we

obtain the following allowed values of k : _ 277-n L (12-3) n = a

**vector**whosecomponents are 0, ±1, ±2, . . . Thus the number of allowed momentum values

between k and k + dk is — 4nk'dk (12.4) (277)3 Photons obey Bose statistics, for

they are indistinguishable and there can be any number of photons with the

same k and ...

Page 258

The state of the lattice in which one phonon is present corresponds to a sound

wave of the form ee«kr-'»o (1222) where the propagation

magnitude |k| = - (12.23) c in which c is the velocity of sound. f Thejjolarization

three_independent directions, coiresponding.to one longitudinal moJe.

oLcarnpiessjon^aye * In as much as anharmonic forces between atoms, which at

high temperatures allow the lattice to ...

The state of the lattice in which one phonon is present corresponds to a sound

wave of the form ee«kr-'»o (1222) where the propagation

**vector**k has themagnitude |k| = - (12.23) c in which c is the velocity of sound. f Thejjolarization

**vector**e is not necessarjjy_^rj>enjdicixlar_ to k. Thus it can havethree_independent directions, coiresponding.to one longitudinal moJe.

oLcarnpiessjon^aye * In as much as anharmonic forces between atoms, which at

high temperatures allow the lattice to ...

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### Contents

THE LAWS OF THERMODYNAMICS | 3 |

SOME APPLICATIONS OF THERMODYNAMICS | 33 |

THE PROBLEM OF KINETIC THEORY | 55 |

Copyright | |

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### Common terms and phrases

absolute zero approximation atoms average Boltzmann transport equation Bose gas Bose-Einstein condensation bosons boundary condition calculation classical collision configuration consider constant coordinates corresponds cosh curve defined denoted density derivation diagonal distribution function eigenvalues electron energy levels entropy equilibrium excited expansion external Fermi gas fermions finite fluid formula given grand canonical ensemble graph Hamiltonian hard-sphere Helmholtz free energy Hence ideal Bose gas ideal Fermi gas ideal gas independent integral interaction interparticle Ising model isotherm law of thermodynamics liquid He4 low temperatures macroscopic magnetic field mass matrix elements Maxwell-Boltzmann distribution microcanonical ensemble molecules momentum number of particles obtain occupation numbers phase transition phonons Phys potential pressure properties pseudopotentials QN(V region satisfies shown in Fig sinh solution specific heat spin statistical mechanics superfluid theorem theory thermodynamic functions valid vector velocity virial wave function