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RIGOROUS RESULTS IN NONEQUILIBRIUM STATISTICAL
STATISTICAL MECHANICAL BASIS
ON THE STATISTICAL MECHANICS OF MODERATELY DENSE
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assumption Auger Effect band Bloch Bloch functions calculation classical coefficients commute consider contribution coordinates corresponding defined denoted density matrix density operator derived described diagonal diamagnetism discussion distribution function dynamical effects eigenfunctions eigenvalues electric field electrons energy ensemble equation of motion equilibrium ergodic evolution expansion expectation value expression Figure finite formal formula frequency give Hamiltonian Hermitian initial integral kinetic equation lattice vibrations lecture linear Liouville macroscopic magnetic field mathematical matrix elements measurement molecules momentum observable obtained occur orbital particle three perturbation phase space phonon Phys physical potential probabilities problem processes projection operator properties quantity quantum mechanics quantum theory Reference result rotational satisfy scattering interaction simple solid spectrum spin spin-lattice coupling statistical matrix Statistical Mechanics successive binary collisions symmetric theorem time-smoothed tion tonian transitions unperturbed variables Wannier functions wave function wave vector Wigner operator Wigner representation zero