Natural analog to cosmology in basic condensed matter physics

We show that the spatially homogeneous and isotropic evolution of a macroscopic Coulomb system of identical particles obeys equations that have the structure of the cosmological equations of the general theory of relativity. There is a Hubble law, and the background charge (if present) mimics the effect of a negative cosmological constant. Specifically, Coulomb explosions mimic the nonsingular open cosmologies in negatively curved spaces, while breathing modes in conductors model oscillatory universes including the anti–de Sitter space.

Figure 1

Evolution of the electron density $n\left(t\right)$ according to Eq. (37) in units given by Eqs. (34) and (35) without positively charged background. The electron liquid contracts for $t<0$ until it reaches the maximal density at $t=0$ followed by an expansion for $t>0$.

Figure 2

Potential well $U\left(a\right)$ (41) for a particle of position $a$ and energy $\epsilon$ in units of Eq. (38). If $\epsilon ⩾1/2$ the motion is finite with turning points $a_{1,2}$ given by solutions to the equation $U\left(a\right)=\epsilon$. Grayscale region is not accessible for the motion.