Narrow Results

The ideas of Mitus et al. are exploited to define the liquid state as a state of matter, in which particles perform locally ordered motion. The presence of the liquid phase is accounted for by a stochastic term in the Hamiltonian, which simulates this property of a liquid. The Bogoliubov–Lee–Huang theory of He II, recently modified by use of effective temperature scale and more stringent reduction procedure (DHSET theory) is extended, by incorporating this term into the ⁴He Hamiltonian. The resulting thermodynamics accounts for effects, which are beyond the scope of other He I and He II theories, e.g., the atomic momentum distribution and excitation spectrum have the form of diffused bands, similarly as in He II; the He I, theoretical heat capacity C_V(T) is a convex function, with a minimum at T_min > T_λ, which qualitatively simulates experimental He I heat capacity. Other thermodynamic functions are similar to those of DHSET theory.

The Bogoliubov-Lee-Huang theory of superfluid ⁴He is modified by introducing an effective temperature scale (which accounts for the deep well of the interatomic potential) and by incorporating into the Hamiltonian a stochastic term V_l, which simulates liquidity of HeI and liquidity of the normal and superfluid component of HeII. V_l depends on two independent random angles α_n, α_s ∈ [0, π], which characterize the locally ordered motion of the two fluids (the normal fluid and superfluid) comprising HeII. The resulting thermodynamics improves the thermodynamic functions and excitation spectrum Ep(α_n, α_s) of the superfluid phase, obtained previously, leaving the heat capacity C_V (T) of the normal phase, with a minimum at T_min > 2.17K, unchanged. The theoretical velocity of sound in HeII, equal to the initial slope of Ep(π, π), agrees with experiment.