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Aspects of reactive moderately dense gas quantum kinetic theory

University of British Columbia

This thesis consists of three parts. In Part I, a two-Liouville space theory of reactive gases is formulated in an effort to understand and by-pass the strong orthogonality approximation standardly used in reactive gas kinetic theories. The formulation is based on a two-Liouville space scattering formalism developed in this thesis. The present work follows an approach very similar to the presentation by Lowry and Snider (J. Chem. Phys. 61, 2320 (1974)). Kinetic equations for arbitrary bound clusters are derived within the structure of the two-Liouville space scattering theory. Bound clusters for an arbitrary number of particles are systematically treated in the present work and defined as the asymptotic bound fragments in the N-particle asymptotic Liouville space. A method of closure, which is quite different from the conventional BBGKY procedure, is introduced to yield a compact set of kinetic equations for the clusters. A comparison with the Lowry-Snider theory is given. In Part II, a Hilbert-Schmidt representation of Ursell operators is given. It is found that the connected quantum Ursell operators are closely related to the Hilbert-Schmidt kernel of Faddeev (for three particles), and its generalization to the description of the collision of an arbitrary number of particles. This important feature permits the formulation of a general Hilbert-Schmidt representation of Ursell operators by expressing the latter in terms of Hilbert- Schmidt kernels. As a consequence, it is seen how the virial coefficients can be evaluated using Hilbert-Schmidt expansions. In particular, second virial coefficient is explicitly expressed in terms of the Hilbert-Schmidt expansion of the resolvent operator. Square integrable states associated with the resonance poles have been found of use in carrying out this expansion. The method depends on distinguishing between the functional analysis properties of the resolvent operator and the analytic function properties of its matrix elements. In Part III, a renormalized quantum Boltzmann equation (R. F. Snider, J. Stat. Phys. 61, 443 (1990)) has been generalized to include the presence of bound states. This has involved the introduction of three coupled equations, one each for the renormalized particle, the bound pair and the unbound pair correlations. The latter is responsible, at equilibrium, for the unbound part of the second virial coefficient. Chapman Enskog solutions to this set of equations are obtained in two schemes. One for moderately dense gas in which there are no bound states, the other in the presence of bound states. The Wigner representation for quantum mechanical operators are used throughout to separate the macroscopic and microscopic properties of the state of system. The resulting expressions for the transport coefficients in the first scheme have contributions arising from particles that are free and from pair correlations. In the second, there are also contributions from the bound pairs.

Thesis/Dissertation

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2009-03-19

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http://hdl.handle.net/2429/6218

Chemistry

University of British Columbia

UBCV

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