Thermal fluctuations of the pionic field and π-condensation in nuclear matter

In presence of the ππ interaction the pionic field is investigated in the isosymmetrical nuclear matter for a nonzero temperature T and a high density rho, at which softening of the pionic degree of freedom occurs and an appearance of the π-condensate instability is possible. A model is proposed to describe thermodynamical fluctuations of the pionic field near the critical point of the π-condensation. It is shown that the account of the fluctuations changes the situation qualitatively; the usual criterion of the π-condensation, as the second-kind phase transition (existence of solutions #betta#2(k) < 0 for the equation D-1 (#betta#, k, rho, T)=0, where D is the pion propagator in the nuclear matter) is no longer valid. The conditions of the π-condensation are determined by the requirement on minimum of the thermodynamical potential, min Ω lte 0 a) a nonzero condensate field phisup(a). The mutual interaction of the pionic excitations, and their interaction with phisup(a) determine the type of the π-condensate transition: is the phase transition first-kind or second-kind. The critical density rhosub(c)(T) and the condensate field are estimated. It was found that the presence of the thermodynamical fluctuations results in an increase in teh critical density by a quantity δrhosub(c)(T), rising rapidly with the temperature, so the matter becomes more stable against the π-condensation at T not equal to a. Possible experimentally observable consequences of increasing fluctuations of the pionic field near the critical point are discussed