ON THE MICROSCOPIC DETERMINATION OF TRANSPORT COEFFICIENTS

Journal Article · Sun Apr 01 04:00:00 EST 1962 · Dissertation Abstr.

OSTI ID:4805023

Swenson, R J

The formal expressions for transport coefficients which are obtained in the ensemble theory of irreversible processes are investigated and a method for reducing them to more practical forms is proposed. To this end, a manybody theory is developed which makes use of a perturbation expansion in terms of a scattering matrix or t-matrix, rather than the potential, and is thus immediately applicable to situations in which the interaction potential contains a hard core. A transport coefficient is related to a time integral of a microscopic correlation function whose time dependence is described by the non-Markovian generalized master equation of van Hove. A simplified derivation of this equation is given and the quantities which appear in it are expressed in terms of the t-matrix. In general the evaluation of a transport coefficient requires that non-Markovian effects be taken into consideration. It is shown that transport coefficients for a system in a quasi-steady state can be determined from the generalized Pauli equation (which is a Markovian equation) which is derived from the generalized master equation. The density dependence of the various quantities which appear are analyzed and the Pauli equation and the expression for the transport coefficient are obtained in the limit of low density. It is demonstrated that in this limit the N-body dependence of the equations can be reduced to a one-body dependence, and in fact, the results are identical to those obtained using the Boltzmann transport equation. These results are obtained without performing coarse-graining or time-smoothing operations or assuming molecular chaos, whereas these are required in the usual derivations of the Boltzmann equation. As an example, the formalism is applied to the thermal conductivity of a dilute non-degenerate quantum gas, and the result obtained agrees with the Boltzmann equation result.

• Research Organization: Lehigh Univ., Bethlehem, Penna.
• NSA Number: NSA-16-024921
• OSTI ID: 4805023
• Journal Information: Dissertation Abstr., Journal Name: Dissertation Abstr. Vol. Vol: 22
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

BOLTZMANN EQUATION
DENSITY
DIFFERENTIAL EQUATIONS
EQUATIONS
GASES
HARD-CORE POTENTIAL
INTERACTIONS
MANY BODY PROBLEM
MARKOV PROCESS
MATRICES
PAULI PRINCIPLE
PERTURBATION THEORY
PHYSICS
QUANTUM MECHANICS
SCATTERING
T-MATRIX
THERMAL CONDUCTIVITY
THERMODYNAMICS
TRANSPORT THEORY