The interfacial profiles and interfacial tensions of phase-separated binary mixtures of Bose-Einstein condensates are studied theoretically. The two condensates are characterized by their respective healing lengths and £2 and by the interspecies repulsive interaction K. An exact solution to the Gross-Pitaevskii (GP) equations is obtained for the special case I 2/ I 1 = 1/2 and K = 3/2. Furthermore, applying a double-parabola approximation (DPA) to the energy density featured in GP theory allows us to define a DPA model, which is much simpler to handle than GP theory but nevertheless still captures the main physics. In particular, a compact analytic expression for the interfacial tension is derived that is useful for all f ,, | 2, and K. An application to wetting phenomena is presented for condensates adsorbed at an optical wall. The wetting phase boundary obtained within the DPA model nearly coincides with the exact one in GP theory.

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The Cornwall-Jackiw-Tomboulis (CJT) effective action for composite operators at finite temperature is used to investigate the chiral phase transition within the framework of the linear sigma model as the low-energy effective model of quantum chromodynamics (QCD). A new renormalization prescription for the CJT effective action in the Hartree-Fock (HF) approximation is proposed. A numerical study, which incorporates both thermal and quantum effect, shows that in this approximation the phase transition is of first order. However, taking into account the higher-loop diagrams contribution the order of phase transition is unchanged.

The phase structure of the linear sigma model at finite isospin chemical potential μ and temperature T is systematically studied in the non-standard case of symmetry breaking by means of the Cornwall-Jackiw-Tomboulis effective potential. The latter quantity is calculated in the improved Hartree-Fock approximation which preserves the Goldstone theorem and the thermodynamic consistency. It results that the charged pions are condensed for μ equal to the pion mass in vacuum and the pion condensation corresponds to a first-order phase transition for 0 T 175.813 MeV, whereas at higher temperature it becomes a second-order phase transition. Moreover, the chiral-symmetry restoration, which is a first-order phase transition, occurs for 138.464 MeV T 147.168 MeV. The phase diagrams for both pion and chiral condensates are obtained.

Basing on the Cornwall-Jackiw-Tomboulis effective action approach we formulate a theoretical formalism for studying kaon condensation in the linear sigma model at finite density and temperature. We derive the renormalized effective potential in the Hartree-Fock approximation, which preserves the Goldstone theorem. This quantity is then used to consider physical properties of kaon matter.

The localized low-energy interfacial excitations, or Nambu-Goldstone modes, of phase-segregated binary mixtures of Bose-Einstein condensates are investigated analytically by means of a doubleparabola approximation (DPA) to the Lagrangian density in Gross-Pitaevskii theory for a system in a uniform potential. Within this model analytic expressions are obtained for the excitations underlying capillary waves or "ripplons" for arbitrary strength K (> 1) of the phase segregation.The dispersion relation ω ∝ k 3/2 is derived directly from the Bogoliubov-de Gennes equations in limit that the wavelength 2π/k is much larger than the healing length ξ. The proportionality constant in the dispersion relation provides the static interfacial tension. A correction term in ω(k) of order k 5/2 is calculated analytically, entailing a finite-wavelength correction factor (1 +). This prediction may be tested experimentally using (quasi-)uniform optical-box traps. Explicit expressions are obtained for the structural deformation of the interface due to the passing of the capillary wave. It is found that the amplitude of the wave is enhanced by an amount that is quadratic in the ratio of the phase velocity ω/k to the sound velocity c. For generic asymmetric mixtures consisting of condensates with unequal healing lengths an additional modulation is predicted of the common value of the condensate densities at the interface.

The phase structure of symmetric nuclear matter in the extended Nambu-Jona-Lasinio (ENJL) model is studied by means of the effective potential in the one-loop approximation. It is found that chiral symmetry gets restored at high nuclear density and a typical first-order phase transition of the liquid-gas transition occurs at zero temperature, T = 0, which weakens as T grows and eventually ends up with a second-order critical point at T = 20 MeV. This phase transition scenario is confirmed by investigating the evolution of the effective potential versus the effective nucleon mass and the equation of state.