Calculations of equilibrium anharmonic properties in bravais with application to the Wigner electron solid
Kugler, Alfred Adam
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https://hdl.handle.net/2142/16593
Description
Title
Calculations of equilibrium anharmonic properties in bravais with application to the Wigner electron solid
Author(s)
Kugler, Alfred Adam
Issue Date
1968
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
equilibrium anharmonic properties
Language
en
Abstract
"A self-consistent method for determining equilibrium properties of Bravais crystals is derived from a variational principle for the free energy, first for the independent oscillator model of a solid, then for the general case of dispersion. The method leads to a set of self-consistent equations which are identical with those derived by Choquard in the ""RHA,"" (renormalized harmonic approximation) using ring diagram summation of the cumulant expansion for the free energy.
A particular approximation is shown to lead to a simpler set of equations which can properly be termed ""Hartree approximation with dispersion,"" and which in some cases offer a suitable alternative to the harmonic approximation as a starting point in carrying out calculations.
Some higher order anharmonic effects are treated on the basis of Choquard's generalized self-consistent equations; in particular, their contributions to the free energy and dynamical self-energy matrix are calculated.
The above theories and methods are applied to the electron solid at T=O. The Hartree approximation is solved, and self-consistent calculations in second order are carried out. In both cases, the effects of anharmonicity on the frequencies are found to be large, and are responsible for bringing about a dynamical instability of the lattice.
Various results obtained previously in the harmonic approximation and in second order perturbation theory are reviewed to facilitate comparison with the self-consistent theories."
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