Complex conductivity in strongly fluctuating layered superconductors

The time-dependent Ginzburg-Landau approach is used to calculate the complex fluctuation conductivity in layered type-II superconductor under magnetic field. Layered structure of the superconductor is accounted for by means of the Lawrence-Doniach model, while the nonlinear interaction term in dynamics is treated within self-consistent Gaussian approximation. In high-$T_{c}$ materials, large portion of the $H-T$ diagram belongs to vortex liquid phase. The expressions summing contributions of all the Landau levels are presented in explicit form which are applicable essentially to the whole phase and are compared to experimental data on high-$T_{c}$ superconductor YBa$_{2}$Cu$_{3}$O$_{7-\delta }$. Above the crossover to the "normal phase", our results agree with the previously obtained.