MEAN-FIELD SOLUTION OF THE CONTINUUM FROHLICH PROBLEM AT FINITE-TEMPERATURE

The temperature behavior of the charge-density-wave (CWD) state in one -dimensional conductor is studied within the framework of a mean-field approach using the exact solution of the self-consistent equations. T he properties of the CDW condensate are found to be dependent on the v alue of the dimensionless parameter which includes an electron-phonon coupling constant and the density of electrons. The thermal behavior o f the CDW is shown to be similar to that of the Bardeen-Cooper-Schrief fer (BCS) superconducting condensate only at sufficiently weak electro n-phonon coupling or relatively high electron density. In the case of comparatively strong coupling or sufficiently low electron density, th e correct mean-field consideration leads to violation of the BCS relat ion between the phase transition temperature and electronic gap at T = 0, and also to a variation of the CDW period, which decreases with in creasing temperature.