Time-Dependent Correlations in a Maxwell Gas

The Fourier transform of the time-dependent density-density correlation function is calculated from the linearized Boltzmann equation for Maxwell molecules. The initial value problem is solved numerically for a small density disturbance. The results are compared with relaxation-time kinetic models, and it is found that the triple-relaxation time model with eigenvalue ordering gives good agreement for all wavelengths and frequencies. Similar macroscopic responses can also be calculated with appropriate changes in the initial conditions. The heat-heat correlation function is considered as a specific example.