Elementary excitations in dilute gases

Abstract

In solids, elementary excitations of atomic vibrations are identified in reciprocal space by their frequency and wavevector as phonons. At the opposite end of the matter spectrum, dynamics of dilute gases is conventionally described in terms of atomic or molecular collisions and translations in real space and time. These two formalisms are apparently incompatible, leading to difficulties in understanding atomic dynamics in intermediate matter. In this work, we demonstrate that normal modes, often synonymously considered as phonons in solids, provide a microscopic description of various transport processes, including thermal conductivity, diffusion coefficient, and shear viscosity, in a prototypical dilute gas, argon. Our results reveal that normal modes constitute elementary excitations in dilute gases, extending their physical relevance far beyond vibrational excitations in solids.

Figures (4)

• Figure 1: Representative temperature dependent normal mode densities of states of dilute argon gas at 200 K (blue curves), 500 K (purple curves), and 800 K (red curves). Nearly equal number of imaginary and real modes are observed at all temperatures, expected of a gas phase. Temperature dependent mass density at 1 bar (brown circle) is shown in Inset along with NIST suggested measurement values (dashed curve) lemmon_thermophysical_2010. Errorbars are smaller than the markers.
• Figure 2: (A) Normalized, individual mode kinetic energy autocorrelation for two modes, -0.124 GHz (black curve) and 0.41 GHz (gray curve) for argon at 500 K. Red dashed curves are exponential decay fits where mode lifetimes are extracted. (B) Probability density function of normal mode lifetimes at 200 K (blue), 500 K (purple), and 800 K (red). Increase in lifetimes with temperature are shown.
• Figure 3: Temperature dependent lifetime comparisons. Black, orange, and yellow circles represent heat current autocorrelation function, mean normal mode, and velocity autocorrelation function lifetimes, respectively. Dashed curve shows a $\sqrt{T}$ dependence, expected for an ideal gas. We see nearly overlapping lifetimes for all temperatures studied here.
• Figure 4: Isobaric thermal conductivity (A) and shear viscosity (B) from 200 K to 800 K at 1 bar for argon gas. Blue circles are from our normal mode calculations and dashed curves are measurement values from NIST lemmon_thermophysical_2010. We observe an excellent agreement between our calculations and measurements within a few percent.