Eigenfunctions for Liouville Operators, Classical Collision Operators, and Collision Bracket Integrals in Kinetic Theory

In the kinetic theory of dense fluids the many-particle collision bracket integral is given in terms of a classical collision operator defined in the phase space. To find an algorithm to compute the collision bracket integrals, we revisit the eigenvalue problem of the Liouville operator and re-examine the method previously reported[Chem. Phys. 20, 93(1977)]. Then we apply the notion and concept of the eigenfunctions of the Liouville operator and knowledge acquired in the study of the eigenfunctions to obtain alternative forms for collision integrals. One of the alternative forms is given in the form of time correlation function. This form, on an additional approximation, assumes a form reminiscent of the Chapman-Enskog collision bracket integral for dilute gases. It indeed gives rise to the latter in the case of two particles. The alternative forms obtained are more readily amenable to numerical simulation methods than the collision bracket integras expressed in terms of a classical collision operator, which requires solution of classical Lippmann-Schwinger integral equations. This way, the aforementioned kinetic theory of dense fluids is made more accessible by numerical computation/simulation methods than before.Comment: 34 pages, no figure, original pape

On the Onsager--Wilson Theory of Wien Effect on Strong Binary Electrolytes in a High External Electric Field

In this review paper, we present and critically re-examine the formal expressions for the electrophoretic effect and the ionic field appearing in the unpublished Yale University PhD dissertation of W. S. Wilson which form the basis of the Onsager--Wilson theory of the Wien effect in the binary strong electrolyte solutions. It is pointed out that some of the integrals that make up the flow velocity formula obtained in the thesis and he evaluated at the position of the center ion in the ionic atmosphere (i.e., the coordinate origin) diverge. Therefore they cannot be evaluated by means of contour integrals in the manner performed in his thesis for the reason pointed out in the text of this paper. In this paper, the results for the integrals in question are presented, which are alternatively and exactly evaluated. The details will be described in the follow-up paper presented elsewhere together with the improved formula for the Wien effect on conductivity.Comment: 46 pages, no figure, tutorial review of the Onsager-Wilson theory of conductance in strong binary electrolyte

Compressive pressure, spatial confinement of ions, and adiabatic heat generation in binary strong electrolyte solutions by an external electric field

In this paper, we make use of the exact hydrodynamic solution for the Stokes equation for the velocity of a binary ionic solution that we have recently obtained, and show that the nonequilibrium pressure in an electrolyte solution subjected to an external electric field can be not only compressive, but also divergent in the region containing the coordinate origin at which the center ion of its ion atmosphere is located. This divergent compressive pressure implies that it would be theoretically possible to locally confine the ion and also to adiabatically generate heat in the local by means of the external electric field. The field dependence of pressure and thus heat emission is numerically shown and tabulated together with the theoretical estimate of its upper bound, which is exponential with respect to the field strength. It shows that, theoretically, the Coulomb barrier between nuclei in the electrolyte solution (e.g., the ion and a nucleus of the solvent molecule) can be overcome so as to make them fuse together, if no other effects intervene to prevent it.Comment: 16 pages, 3 figures, 1 tabl

Transport coefficients from the Boson Uehling-Uhlenbeck Equation

We derive microscopic expressions for the bulk viscosity, shear viscosity and thermal conductivity of a quantum degenerate Bose gas above $T_C$, the critical temperature for Bose-Einstein condensation. The gas interacts via a contact potential and is described by the Uehling-Uhlenbeck equation. To derive the transport coefficients, we use Rayleigh-Schrodinger perturbation theory rather than the Chapman-Enskog approach. This approach illuminates the link between transport coefficients and eigenvalues of the collision operator. We find that a method of summing the second order contributions using the fact that the relaxation rates have a known limit improves the accuracy of the computations. We numerically compute the shear viscosity and thermal conductivity for any boson gas that interacts via a contact potential. We find that the bulk viscosity remains identically zero as it is for the classical case.Comment: 10 pages, 2 figures, submitted to Phys. Rev.

Cluster expansion for transport coefficients for dense simple fluids

Cluster expansions are presented for the collision bracket integrals for transport cofficients of a dense simple fluid which appear in the kinetic theory of dense fluid reported previously. The density series calculated with the cluster expansions are given in exponential forms and their leading terms consist of a connected three-particle collision operator. The three-particle contributions are discussed in terms of mass-normalized coordinates which make it possible to put them in forms structurally rather similar to the two-particle collision bracket integrals in the Chapman-Enskog theory. The three particle contributions are thus cast into forms suitable for numerical computation