Phase Transition in Bose Liquid. I
Progress of theoretical physics
We show that the Bose liquid can be worked out in a way similar to the Landau Fermi liquid theory by decomposing the diagonal elements of the Boltzmann factor for the system into irreducible diagrams. The energy of the system is expressed by the functional of the occupation number n 1 r The excitation energy is defined by the variation of the energy with respect to np. The Landau f-functions (the second variations of the energy) are closely related to the excitation energy and play important
... d play important roles in the phase transition. The excitation-energy dependence of Landau f-functions are obtained for the dilute gas. Jp + kJ 2 r-s where r is the exponent of the excitation energy epocpr (see § 6). We believe that there are several points to be reconsidered in PP's theory.*> Let us now turn to what we shall do in the present paper. We work out the interacting Bose gas in a similar way to Landau Fermi liquid theory. 20 > We shall show that the free energy is expressed by the functional of the occupation number np. The excitation energy, ep, is defined by the variation of the energy with respect to npo The Landau !-functions (the second variations of the energy) are closely related to the excitation energy and play important roles in the phase transition. The relation between the excitation energy and the Landau !-functions will be obtained. *> Recently Migdal18l has pointed out that PP's theory contains an inconsistency and Ep is not proportional to pS/2• The present author19> has, however, found that Migdal's theory does not give the logarithmic singularity.