| Summary: | 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. === Science, Faculty of === Chemistry, Department of === Graduate
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