A Classical Luttinger liquid

Abstract

We propose a binary nonadditive Asakura-Oosawa-like mixture as an example for the classical limit of a Luttinger liquid. We determine the equation of state and structure of this mixture and discuss the paradoxical situation that one faces when working with a quantum liquid without a ground state. We then propose a new class of one dimensional classical fluids.

Figures (2)

• Figure 1: Compressibility factor $Z=\beta P/\rho$ for the nonadditive nearest neighbor hard rods binary mixture described in the text. $\beta=1/k_BT$ where $k_B$ is Boltzmann constant, $T$ is the absolute temperature, $P$ is the pressure, $\rho=(N+M)/L$ is the density, $x_1=N/(N+M)$ is the molar fraction of the particles of species "1", and $x_2=1-x_1$. The continuous line shows the result for the symmetric mixture and the dashed line the one for an asymmetric one.
• Figure 2: Partial radial distribution functions (like, $g_{11}$ and $g_{22}$, and unlike, $g_{12}$) as functions of $r=|x|$ for the nonadditive nearest neighbor hard rods binary mixture described in the text at a density $\rho=0.8$. Of course $g_{12}(r)$ vanishes for $r<\sigma_{12}=1$. We show the result for the two mixture already considered in Fig. \ref{['fig:eos']}. Clearly in the symmetric mixture $g_{11}=g_{22}$.