## Coherent state and its application to quantum statistical mechanics |

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### Contents

MATHEMATICAL PRELIMINARIES | 4 |

EQUILIBRIUM QUANTUM STATISTICAL MECHANICS | 9 |

NONEQUILIBRIUM QUANTUM STATISTICAL MECHANICS | 21 |

2 other sections not shown

### Common terms and phrases

anharmonic solid Boltzmann equation Brout-Prigogine equation Brownian motion calculate Chapter classical mechanics coherent state representation coherent states d.f. complex numbers consider coordinates and momenta denote density matrix destruction operators dj J p(J equation of motion exp i j expansion exponential expression f{vj ffof given by Eq group velocity Hamiltonian Hence higher order inhomogeniety inner product integral in Eq interaction interaction picture JkJk'Jk kk'k lattice Liouville equation Mori non-equilibrium statistical mechanics normal modes number of phonons occupation number particles Peierls equation Phys positive definite priori phases assumption q+ and q quantum correction quantum mechanical system QUANTUM STATISTICAL MECHANICS random a priori rate of change reduced matrix element result satisfy the commutation sharp brackets side of Eq system of phonons Taylor series thermodynamic equilibrium transport equation variables Vkk'k wave packet Wigner d.f. Wigner distribution function