Plasma resonance and remaining Josephson coupling in the ''decoupled vortex liquid phase'' in layered superconductors

We relate the frequency of the Josephson plasma resonance in layered superconductors with the frequency dependent superconducting response. We demonstrate that the sharp resonance can persist even when the global superconducting coherence is broken provided the resonance frequency is larger than the frequency of interlayer phase slips. In this situation the plasma frequency is determined by the average Josephson energy, which can be calculated using the high temperature expansion. We also find the temperature dependence of the average Josephson energy from the Monte Carlo simulations and determine the applicability region of the high temperature expansion.