Elasticity of an electron liquid

The zero-temperature response of an interacting electron liquid to a time-d ependent vector potential of wave vector q and frequency omega, such that q much less than q(F), qvF much less than omega E(F)much less than E-F/(h) o ver bar (where q(F), v(F), and E-F are the Fermi wave vector, velocity, and energy, respectively), is equivalent to that of a continuous elastic mediu m with nonvanishing shear modulus mu, bulk modulus K, and viscosity coeffic ients eta and zeta. We establish the relationship between the viscoelastic coefficients and the long-wavelength limit of the "dynamical local-field fa ctors" G(L(T))(q, omega), which are widely used to describe exchange-correl ation effects in electron liquids. We present several exact results for mu, including its expression in terms of Landau parameters, and practical appr oximate formulas for mu, eta, and zeta as functions of density. These are u sed to discuss the possibility of a transverse collective mode in the elect ron liquid at sufficiently low density. Finally, we consider impurity scatt ering and/or quasiparticle collisions at nonzero temperature. Treating thes e effects in the relaxation-time (tau) approximation, explicit expressions are derived for mu and eta as functions of frequency. These formulas exhibi t a crossover from the collisional regime (omega tau much less than 1), whe re mu similar to 0 and eta similar to nE(F)tau, to the collisionless regime (omega tau much greater than 1), where mu similar to nE(F) and eta similar to 0. [S0163-1829(99)02632-6].