5 FIG. 2: (color online) The chemical potential µ (in units of n 2 / $^{3}$/ (2 m )) as a function of ν = − 1 /a$_{s}$ (in units of n 1 / $^{3}$) for given atom density n . FIG. 3: (color online) The pressure P (in units of n 5 / $^{3}$/ (2 m )) as a function of ν = − 1 /a$_{s}$ (in units of n 1 / $^{3}$) for given atom density n . FIG. 4: (color online) The sound velocity v$_{s}$ (in units of n 1 / $^{3}$/ (2 m )) as a function of ν = − 1 /a$_{s}$ (in units of n 1 / $^{3}$) for given atom density n . −2 −1 0 1 2 6 8 10 12 14 16 18 20 −2 −1 0 1 2 2.5 3 3.5 4 4.5 5 P −2 −1 0 1 2 3 3.2 3.4 3.6 3.8 4 4.2 4.4 v s Eq. (11), we get the free energy density for the ASF state From the thermodynamical relation n = − ( ∂f/∂µ ), we find that where n is the density of (bare) atoms and Using Euler’s relation f = − P , we get the equation of state at T = 0 for the ASF phase with µ as a function of n and δ given by Eq. (24). Fi- nally, we may calculate the sound velocity v$_{s}$ through the relation v 2 s = ( n/m ) ∂µ/∂n , and obtain with µ as a function of n and δ given by Eq. (24). The atom density n gives rise to a characteristic length scale n − 1 /d and a characteristic energy scale n 2 $^{/d}$/ (2 m ). By measuring the lengths and energies in units of these characteristic scales, setting d = 3, and using Eq. (10) to replace δ by ν , Eqs. (24), (25), and (26) can be written as where x = bmδa$_{0}$n − 1 / 3 = n − 1 / $^{3}$ν with ν = − 1 /a$_{s}$ , b = 2 /π and y = 2 mµn − 2 / $^{3}$, and where ˜ P = 2 mn − 5 / $^{3}$P and ˜ v$_{s}$ = 2 mv$_{s}$n − 1 / $^{3}$. Equations (27) — (29) exhibit the universal scaling forms for µ , P and v$_{s}$ . These universal scaling forms are due to the presence of a nontrivial zero-density fixed point. The results are shown in Figs. 2, 3, and 4. In the unitary limit δ = 0 Eqs. (24) and (25) reduce to f$_{ASF}$ = − K$_{d}$ 4 ϵ (2 m ) 2 − ϵ 2 µ 3 − ϵ 2 + K$_{d}$ 8 ϵ a ϵ $_{0}$δ (2 mµ ) 2 . (23) n = C $_{d}$(2 mµ ) d 2 { 1 − 1 3 − ϵ/ 2 [ 2 mδa ϵ 0 (2 mµ ) d $_{2}$− 1 ]} , (24) C d = K$_{d}$ (3 − ϵ/ 2) 4 ϵ . P = K$_{d}$ 4 ϵ (2 m ) d/ $^{2}$µ1+ d/ 2 [ 1 − mδa ϵ 0 (2 mµ ) d/ 2 − 1 ] , (25) v 2 s = 2 µ dm [ (3 − ϵ/ 2)(2 mµ ) d/ 2 − 1 − 2 mδa ϵ 0 (3 ϵ/ 2)(2 mµ ) d/ 2 − 1 4 mδa ϵ $_{0}$/d ] , (26) 16 π 2 5 = y 3 / 2 − 2 π 5 xy , (27) ˜ P = 1 8 π 2 ( y 5 / 2 − π 2 xy 2 ) , (28) 5 √ y 2 πx ˜ v 2 s = 4 y ( 5 y − 2 πx 15 y 4 πx , (29) µ = 1 2 m ( n C d ) 2 /d , (30)