I will discuss recent results on collective behaviour of N particles repelling each other via pairwise interaction potential and confined by an external harmonic trap. I will discuss the large-N field theory for all-to-all coupling [1] and the finite ranged case [2]. These family of models contain in them various well known systems of interest both in physics and mathematics such as one component plasma, Dyson's log-gas, and the integrable Calogero-Moser model to name a few. I will also present results in the presence of a barrier [3]. I will then discuss gap statistics (analogous to the well known level spacing statistics) in these family of models [4]. In the end, I will present some preliminary results that show how the derived large-N theory can be used to understand collective non-equilibrium dynamics of these interacting particles.

[1] S. Agarwal, A. Dhar, M. Kulkarni, A. Kundu, S. N. Majumdar, D. Mukamel, G. Schehr, Phys. Rev. Lett. 123, 100603 (2019), Editors' Suggestion

[2] A. Kumar, M. Kulkarni, A. Kundu, Phys. Rev. E 102, 032128 (2020)

[3] J. Kethepalli, M. Kulkarni, A. Kundu, S. N. Majumdar, D. Mukamel, G. Schehr, arXiv:2107.00524 (2021)

[4] S. Santra, J. Kethepalli, S. Agarwal, A. Dhar, M. Kulkarni, A. Kundu, S. N. Majumdar, and G. Schehr [in preparation]