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CORRELATION AND RESPONSE FUNCTIONS
GENERALIZED LANGEVIN EQUATION
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approximation autocorrelation function average value behaviour Bose calculation commutator components conserved variable contribution correlation function coupling constant defined delta function denote derived described diagrams dielectric function dimension dimensionless discussion displacement divergence dynamic susceptibility electron fluid energy equation of motion evaluated example expression factor ferromagnetic finite fixed point fluctuations Fourier transform frequency given Green function Hamiltonian Hartree-Fock Heisenberg Hence Hermitian operator identity imaginary integral L-G model Landau Langevin equation Laplace transform lattice limit linear response linear response function long wavelength magnetic field matrix element memory function momentum Navier-Stokes liquid non-interacting obtained parameter particle density perturbation theory phonon Phys Physics potential problem proportional quantity quantum random force relation relaxation function renormalization result RG equation right-hand side S(rr satisfies scattering response function self-energy spin wave statistics sum rule symmetry transport coefficient vanishes velocity wave vector wave vector dependent zero