University of Oulu

Numerical calculations of quasiparticle dynamics in a Fermi liquid

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Author: Virtanen, Timo1
Organizations: 1University of Oulu, Faculty of Science, Department of Physics, Division of Theoretical Physics
Format: ebook
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 6.2 MB)
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Language: English
Published: Oulu : University of Oulu, 2011
Publish Date: 2011-03-08
Thesis type: Doctoral Dissertation
Defence Note: Academic Dissertation to be presented with the assent of the Faculty of Science, University of Oulu, for public discussion in the Auditorium L10, on March 18th, 2011, at 12 o’clock noon.
Reviewer: Professor Mikael Fogelström
Professor Christopher J. Pethick
Opponent: Professor Christopher J. Pethick
Kustos: Professor Erkki Thuneberg


The problem of describing a system of many interacting particles is one of the most fundamental questions in physics. One of the central theories used in condensed matter physics to address the problem is the Fermi liquid theory developed by L. D. Landau in the 1956. The theory describes interacting fermions, and can be used to explain transport phenomena of electrons in metals and dynamics of helium three. Even when the theory is not directly applicable, it forms a basis against which other, more sophisticated theories can be compared.

this thesis the Fermi liquid theory is applied to 3He-4He-mixtures at temperatures where the bosonic 4He part is superfluid, and the mechanical properties of the system are largely determined by the 3He component, treated as a degenerate normal Fermi liquid. The dynamics of strongly interacting liquid 3He can be described as a collection of quasiparticles, elementary excitations of the system, which interact only weakly. In 3He-4He mixtures the interactions can be continuously tuned by changing the temperature and the concentration of the mixture. The scattering time of quasiparticles depends on temperature, and thus the transition from the hydrodynamic limit of continuous collisions at higher temperatures to the collisionless ballistic limit at low temperatures can be studied. This gives invaluable information on the role of the interactions in the dynamics of the system.

In this work, by using the Fermi liquid theory and Boltzmann transport equation, the dynamics of helium mixture disturbed by a mechanical oscillator is described in the full temperature range. The solution necessarily is numeric, but new analytical results in the low temperature limit are obtained as well. The numerical approach enables one to study various boundary conditions thoroughly, and allows application of the theory to a specic geometry. It is shown that in order to explain the experimental observations, it is necessary to take into account the reflection of quasiparticles from the walls of the container. For suitable choice of oscillator frequency and container size, second sound resonances are observed at higher temperatures, while in the ballistic limit quasiparticle interference can be seen.

The numerical results are in quantitative agreement with experiments, thus attesting the accuracy of Fermi liquid theory. In particular, the previously observed decrease of inertia of a mechanical oscillator immersed in helium at low temperatures is reproduced in the calculations, and is explained by elasticity of the fluid due to Fermi liquid interactions.

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Series: Report series in physical sciences
ISSN: 1239-4327
ISSN-L: 1239-4327
ISBN: 978-951-42-9390-0
ISBN Print: 978-951-42-9389-4
Issue: 66
Copyright information: © University of Oulu, 2011. This publication is copyrighted. You may download, display and print it for your own personal use. Commercial use is prohibited.