5.0 GLYPH<Multiply> 10 6 1.0 GLYPH<Multiply> 10 7 1.5 GLYPH<Multiply> 10 7 2.0 GLYPH<Multiply> 10 7 0.07 0.08 0.09 0.10 Attractive fermions PSfrag replacements 1 4 π η/s µ/T FIG. 12: The ratio η/s as a function of µ/T in the limit of very low temperatures (top curve). The horizontal line is 1 / 4 π . The bottom curve is the approximation eq. (79). The limiting values are and As for the fermionic case, the value ˜ ξ = 0 . 842766 = 12 log 2 /π 2 implies the energy per particle ϵ$_{1}$ = T , which means the gas is in the classical limit. The ratio η/s given by the expressions eq. (73) with the appropriate bosonic c and b . We find that η/s has its minimum value at z$_{c}$ , where it is actually below the bound lim µ/T →−∞ ˜ ξ = 0 . 842766 , ˜ ξ ( z$_{c}$ ) ≈ 0 . 39 (91) lim T/µ → 0 − ξ = ∞ , ξ ( z$_{c}$ ) ≈ 2 . 3 (92) η s ≥ 0 . 4 ℏ 4 πk$_{B}$ (93) 32