Diffusion Monte Carlo Calculations of Current Density as Function of Position in Anomalous Transmission of a Helium Beam Through a Slab of Superfluid Helium

Abstract

Bose-Einstein condensation is believed to be the reason for superfluidity in liquid helium-four. Transmission experiments on superfluid helium-four may probe the structure and properties of the condensate. Transmission processes can occur with the excitation of quasiparticles, such as phonons, rotons and ripplons. Those are called quasiparticle-mediated transmissions and have been observed in experiments. It was proposed that superfluid helium transmission may also be mediated by the condensate. It was predicted that in this anomalous transmission process the transmission amplitude would be substantial and the transmission time would be much shorter than that in quasiparticle-mediated transmissions. Condensate-mediated transmission, if observed, would provide a direct probe of the off-diagonal long-range order in superfluid helium. In this thesis I report on Diffusion Monte Carlo simulations of the transmission process. The transmission problem was reformulated in terms of scattering states which are real eigenstates of the operation of reflection and the Hamiltonian. Phase shifts for the scattering states were calculated at various wavevectors and the transmission coefficient as a function of wavevector was found. Previous computational results were compared and confirmed with better accuracy. A fast anomalous transmission process which is mediated by the condensate in superfluid helium is predicted. Those previous calculations used a trial function which did not conserve particle current in the system and a primary objective of the thesis work was to correct that defect. I developed and used a variant of a Diffusion Monte Carlo method previously used to calculate the one-body density matrix for homogeneous bulk superfluid helium to calculate the current density as a function of position. I will present results for the current which indicate that it is much closer to being correctly conserved than it was in the previous reported work.