Archive ouverte HAL – Harmonically Confined Particles with Long-Range Repulsive Interactions

Sanaa AgarwalAbhishek Dhar 1 Manas KulkarniAnupam Kundu 1 Satya N. Majumdar 2 David Mukamel 3 Gregory Schehr 2 S. n. Majumdar

Sanaa Agarwal, Abhishek Dhar, Manas Kulkarni, Anupam Kundu, Satya N. Majumdar, et al.. Harmonically Confined Particles with Long-Range Repulsive Interactions. Physical Review Letters, American Physical Society, 2019, 123 (10), ⟨10.1103/PhysRevLett.123.100603⟩. ⟨hal-02295905⟩

We study an interacting system of $N$ classical particles on a line at thermal equilibrium. The particles are confined by a harmonic trap and repelling each other via pairwise interaction potential that behaves as a power law $\propto \sum_{\substack{i\neq j}}^N|x_i-x_j|^{-k}$ (with $k>-2$) of their mutual distance. This is a generalization of the well known cases of the one component plasma ($k=-1$), Dyson's log-gas ($k\to 0^+$), and the Calogero-Moser model ($k=2$). Due to the competition between harmonic confinement and pairwise repulsion, the particles spread over a finite region of space for all $k>-2$. We compute exactly the average density profile for large $N$ for all $k>-2$ and show that while it is independent of temperature for sufficiently low temperature, it has a rich and nontrivial dependence on $k$ with distinct behavior for \$-2

• 1. International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore
• 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
• 3. Weizmann Institute