1201.1845 (Maksim D. Tomchenko)

Microstructure of He II in the presence of boundaries    [PDF]

Maksim D. Tomchenko

We determine the structure of exact wave functions of the ground (\Psi_0) and excited (\Psi_k) states of He II under zero boundary conditions (BCs). The solutions take the form \Psi_0=(formula) and \Psi_k =(formula 2). The explicit account for boundaries leads to a significant change of the equations for \Psi_0 and \Psi_k and the theoretical values of the energy of quasiparticles E(k) and the energy of the ground state E_0, as compared with the solutions for periodic BCs. In the limit of a weak interaction, we obtain the formula E(k) = \sqrt{(h^{2} k^2/2m)^{2} + [n\nu_{3}(k)/8][h^2 k^2/m]}, which differs from the well-known Bogolyubov formula by the factor 1/8. The effect of boundaries is related to the different collections of eigenmodes for closed and open system. We advance also the idea of the relation of the \lambda-transition to the multiple creation of rotons with zero energy.

View original: http://arxiv.org/abs/1201.1845