Kinetic theory of normal quantum fluids

Chemistry, Kinetic theory, quantum fluids

Smith, Jeffrey Bernard ; Corngold, Noel Robert

University:California Institute of Technology

Department:Chemistry and Chemical Engineering

关键词: Chemistry, Kinetic theory, quantum fluids;   

Others  :  https://thesis.library.caltech.edu/8533/1/Smith-jb-1975.pdf

美国|英语

来源: Caltech THESIS

【 摘 要 】

Close to equilibrium, a normal Bose or Fermi fluid can bedescribed by an exact kinetic equation whose kernel is nonlocal in space and time. The general expression derived for the kernel is evaluated to second order in the interparticle potential. The result is a wavevector- and frequency-dependent generalization of the linearUehling-Uhlenbeck kernel with the Born approximation cross section.

The theory is formulated in terms of second-quantized phase space operators whose equilibrium averages are the n-particle Wigner distribution functions. Convenient expressions for the commutators and anticommutators of the phase space operators are obtained. The two-particle equilibrium distribution function is analyzed in terms of momentum-dependent quantum generalizations of theclassical pair distribution function h(k) and direct correlation function c(k). The kinetic equation is presented as the equation of motion of a two -particle correlation function, the phase space density-density anticommutator, and is derived by a formal closure of the quantum BBGKY hierarchy. An alternative derivation using a projection operator is also given. It is shown that the method used for approximating the kernel by a second order expansion preserves all the sum rules to the same order, and that the second-order kernel satisfies the appropriate positivity and symmetry conditions.