Quark and Gluon Condensates in Isospin Matter

Applying the Hellmann-Feynman theorem to a charged pion gas, the quark and gluon condensates at low isospin density are determined by precise pion properties. At intermediate density around $f_{\pi }^2{m}_{\pi }$, from both the estimation for the dilute pion gas and the calculation with Nambu–Jona-Lasinio model, the quark condensate is strongly and monotonously suppressed, while the gluon condensate is enhanced and can be larger than its vacuum value. This unusual behavior of the gluon condensate is universal for Bose condensed matter of mesons. Our results can be tested by lattice calculations at finite isospin density.