Systems of interacting particles confined in external potentials are ubiquitous in nature. Particularly, pairwise repulsive interactions with power-law singularities have taken a special place in physics and mathematics. I will discuss properties of a class of N particles interacting via pairwise repulsive interaction potential and confined by an external potential which tries to pull them to its minimum. On the other hand the repulsive interaction and the entropy try to spread them apart forcing them to settle down over some region with an inhomogeneous density. I will discuss how the large-N macroscopic description of the system in terms of this density depends on the nature and range of the repulsive interaction, form of the confining potential and external constraints, and how the mean density of particles get affected by these factors.
Zoom link: https://zoom.us/j/98086148556?pwd=cWpxbSsrV3lNanpSY1c0ZUtZbVdRUT09
Meeting ID: 980 8614 8556