text: 16 
  
  of ∆W (ωc) in a system without a lattice (Ref.51). The 
  authors of that work also found that the frequency of zero- 
  crossing of ∆W (ωc) increases with the coupling strength. 
  
  51 Ar. Abanov and A.V. Chubukov, Phys. Rev. B 70, 100504 
  (2004). 