Abstract
The ground-state energies of systems containing up to twelve $$\pi^+$$'s in a spatial volume V ~ (2.5 fm)^3 are computed in dynamical, mixed-action lattice QCD at a lattice spacing of ~ 0.125 fm for four different values of the light quark masses. Clean signals are seen for each ground state, allowing for a precise extraction of both the $$\pi^+\pi^+$$ scattering length and $$\pi^+\pi^+\pi^+$$-interaction from a correlated analysis of systems containing different numbers of $$\pi^+$$'s. This extraction of the $$\pi^+\pi^+$$ scattering length is consistent with than that from the $$\pi^+\pi^+$$-system alone. The large number of systems studied here significantly strengthens the arguments presented in our earlier work and unambiguously demonstrates the presence of a low energy $$\pi^+\pi^+\pi^+$$-interaction. The equation of state of a $$\pi^+$$ gas is investigated using our numerical results and the density dependence of the isospin chemical potential for these systems agrees well with the theoretica
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