Quantum Hard Spheres with Affine Quantization

Abstract

We study a fluid of quantum hard-spheres treated with affine-quantization. Assuming that the fluid obeys to Bose-Einstein statistics we solve for its thermodynamic properties using the path integral Monte Carlo method.

Figures (2)

• Figure 1: We show two snapshots of the paths of 30 AQHS made of 250 timeslices each. At a density $\rho^\star=0.1$ and temperature $T^\star=0.05$. On the left, at the beginning of the simulation started with the paths at random non-overlapping positions repeated for all the $M=250$ beads of each of the $N=30$ paths. On the right, at the end of the simulation when the random walk in the path integral reached equilibrium. During the simulation we measured a kinetic energy per particle $\langle{\cal K}\rangle/Nk_BT=37.0(3)$, a potential energy per particle $\langle{\cal V}\rangle/Nk_BT=-6.72(2)$, and a compressibility factor $\langle{\cal Z}\rangle=97.8(1)$.
• Figure 2: We show the compressibility factor $\langle{\cal Z}\rangle$ as a function of the packing fraction $\eta$ at various values of the temperature, from our numerical results of Table \ref{['tab:nr']}. For comparison, the Carnahan-Starling (CS) equation of state, $Z=(1+\eta+\eta^2-\eta^3)/(1-\eta)^3$, of classical HS Carnahan1969 is also shown as a continuous line. The logarithmic scale on the compressibility factor axis is necessary because of the incompressibility nature of the AQHS fluid at low temperature in his extremely quantum regime.