Transport with noise in dilute gases: Effect of Langevin thermostat on transport coefficients

TL;DR

The paper addresses how a Langevin thermostat alters transport coefficients in dilute gases for hard-core and soft-core interatomic potentials. It combines molecular dynamics simulations with a generalized Ohm's-law framework to decompose transport into a series of Boltzmann (interparticle) and Langevin (bath) conductances, yielding explicit expressions for the reduced coefficients $D^*$, $\eta^*$, and $\lambda^*$ as functions of $t_d^*$, $T^*$, $\rho^*$, and collision integrals $\Omega^{*(i,j)}$. Key contributions include the derivation of Langevin-current transport formulas, the closed-form noise-modified coefficient expressions, and comprehensive MD validation across potentials, demonstrating the ability to extract intrinsic transport properties through $\frac{1}{\mathcal{C}} = \frac{1}{\mathcal{C}_L} + \frac{1}{\mathcal{C}_B}$. The results enable systematic removal of thermostat influence in dilute-gas transport studies and clarify how damping time tunes the balance between bath-dominated and collision-dominated transport.

Abstract

In dilute gases, transport properties such as the thermal conductivity, self-diffusion, and viscosity are significantly affected by interatomic collisions, which are determined by the potential form. This study explores these transport properties in the presence of a Langevin thermostat in systems where particles interact through various potentials, including soft-core and hard-core potentials, both with and without an attractive region. Using molecular dynamics simulations and a theoretical approach based on an analogy with an electric circuit (Ohm's law), we derived and compared the transport coefficients across these interatomic potentials for different couplings with the thermostat. The transport coefficients were obtained by considering the thermostat as a resistance in a series circuit.

Figures (4)

• Figure 1: Scaled interatomic potentials used in this paper, $\Phi/\epsilon$, against distance, $r/\sigma$ ($\epsilon$ and $\sigma$ are characteristic values of energy and distance for each potential). The potentials are pesudo hard spheres (blue line), Lennard-Jones (LJ, green dashed curve), Morse (red dotted curve) and soft spheres (purple dot-dashed curve). Soft spheres and Morse potentials are soft core, while LJ and pseudo hard spheres potentials are hard core (they diverge as $r\rightarrow 0$).
• Figure 2: Diffusion coefficient, $D^*$, against damping time, $t_d^*$ of the Langevin thermostat, in log scale for different potentials: (a) pseudo-hard spheres ($T^*=1.5$) and LJ ($T^*=1.5$ and 4), (b) soft-spheres ($T^*=4$) and Morse ($T^*=1.5$ and 4). Dots are numerical results from MD simulations and the curves are obtained form Eq. \ref{['e.D']} with the collision integrals calculated as explained in the text. For the dotted blue curve for soft-spheres, the value of $\Omega^{*(1,1)}$ was obtained by interpolation. The concentration is $\rho^*=0.01$.
• Figure 3: Viscosity, $\eta^*$, against damping time, $t_d^*$, in log scale for different potentials: (a) pseudo-hard spheres ($T^*=1.5$) and LJ ($T^*=1.5$ and 4), (b) soft-spheres ($T^*=4$) and Morse ($T^*=1.5$ and 4). Dots are MD simulation results and curves are obtained from Eq. \ref{['e.e']}. The concentration is $\rho^*=0.01$.
• Figure 4: Thermal conductivity, $\lambda^*$, against damping time, $t_d^*$, in log scale for different potentials: (a) pseudo-hard spheres ($T^*=1.5$) and LJ ($T^*=1.5$ and 4), (b) soft-spheres ($T^*=4$) and Morse ($T^*=1.5$ and 4). Dots are numerical results from MD simulations and the curves are obtained form Eq. \ref{['e.l']}. The concentration is $\rho^*=0.01$.