Frozen density ansatz

With the frozen density ansatz all terms in parenthesis in the last equation will be zero. The only contribution from F to the adsorption energy difference is therefore the non-local electrostatic energy,... 

In the same way, the frozen potential and density ansatz renders the net contribution from the nv integrals in the kinetic energy difference zero, and only the difference in the one-electron energies calculated with the frozen potentials outlined above will contribute to the kinetic energy contribution ... 

Equation (237) shows that when the coupling constant is larger than the critical value Xc = 1 the ansatz [Eq. (234)] leads to an acceptable solution. This implies that for X < 1, density fluctuations decay to zero for a long time but for X > 1 they decay to a finite value/. The value off increases from/ = 1/2 for X — 1 to / = 1 for X —> oo. Thus the spectrum of density fluctuation exhibits a delta function peak at zero frequency, with strength / which is the characteristic of a glassy phase. Thus in the glass phase the translational motion is frozen in and the vibrational motion around the arrested position is described by (z). 

---