Generalized coherent-state derivation of time-dependent density-functional theory equations for superconductors

Equations of motion are derived for the normal and anomalous single-electron density matrices of a Fermi liquid using a time-dependent finite-temperature generalized coherent-state variational ansatz for the many-body density matrix. Self-consistent equations for the order parameter Delta allow us to investigate the interplay of the Coulomb repulsion and pairing attraction in homogeneous and inhomogeneous Fermi liquids with spontaneously broken symmetry such as high-temperature superconductors. The temperature of the Kosterlitz-Thouless transition to the two-dimensional superfluidity is calculated.