Crossover in density profiles of confined particles in power-law models with finite range of interaction

Saikat Santra, Anupam Kundu

Published 2023-08-23Version 1

We consider a classical system of $N$ particles confined in a harmonic trap in one dimension. The pairwise interaction potential between two particles separated by a distance $r$ is taken to be power-law form, $ V(r) \sim 1/r^k$ known as Riesz gas. We particularly look at the case where the particles can interact up to $d$ particles to its left and right if any. By tuning the values of the parameter $d$, the system can be made from nearest neighbour $(d=1)$ to all-to-all $(d=N-1)$ interaction model, however the scaling function changes dramatically as $f$ is changed. Previous studies inform that the collective theories and the equilibrium densities are different in the two limits. In this article we study the crossover in density profile by tuning the parameter $f(=d/N)$ from $1$ to $0$. We find the system size scaling of the density profile for $f \neq 0$ to be same as it is in the all-to-all coupling case. We have numerically demonstrated the density-crossover for general $k$ and provide our analytical understanding in some special values of $k$ e.g., $k=-1$ and $k \to 0$.