Title Evaluation of specific heat for superfluid helium between 0 - 2

The specific heat of liquid helium was calculated theoretically in the Landau theory [1]. The results deviate from experimental data in the temperature region of 1.3 2.1 K. Many theorists subsequently improved the results of the Landau theory by applying temperature dependence of the elementary excitation energy [2], [3]. As well known, many-body system has a total energy of Galilean covariant form. Therefore, the total energy of liquid helium has a nonlinear form for the number distribution function. The function form can be determined using the excitation energy at zero temperature and the latent heat per helium atom at zero temperature. The nonlinear form produces new temperature dependence for the excitation energy from Bose condensate. We evaluate the specific heat using iteration method. The calculation results of the second iteration show good agreement with the experimental data in the temperature region of 0 2.1 K, where we have only used the elementary excitation energy at 1.1 K. 1. Nonlinear form of total energy Liquid helium system has a total Hamiltonian as H = ∑ p p2 2m apap + 1 2V ∑ p,q,k g(k)ap+ka ∗ q−kapaq (1) where m is the mass of a helium atom, ap and ap respectively signify the creation and annihilation operators. We examine the general form of the total energy via the unitary transformation U diagonalizing the Hamiltonian H. All eigenstates are described as | eigenstate >= Uap1a ∗ p2a ∗ p3 · · · a ∗ pN | 0 > where | 0 > denotes the vacuum state. New creation and annihilation operators are defined as Ap = Ua ∗ pU −1, Ap = UapU (2) which indicate the creation and annihilation operators of a quasi-particle. We designate this quasi-particle as a ”dressed boson”. The dressed boson number operator is defined as np = ApAp. (3) The total number conservation and the total momentum conservation are expressed as 25th International Conference on Low Temperature Physics (LT25) IOP Publishing Journal of Physics: Conference Series 150 (2009) 032091 doi:10.1088/1742-6596/150/3/032091 c © 2009 IOP Publishing Ltd 1