Abstract
We consider a one-dimensional classical Coulomb gas of -like charges in a harmonic potential—also known as the one-dimensional one-component plasma. We compute, analytically, the probability distribution of the position of the rightmost charge in the limit of large . We show that the typical fluctuations of around its mean are described by a nontrivial scaling function, with asymmetric tails. This distribution is different from the Tracy-Widom distribution of for Dyson’s log gas. We also compute the large deviation functions of explicitly and show that the system exhibits a third-order phase transition, as in the log gas. Our theoretical predictions are verified numerically.
- Received 28 April 2017
DOI:https://doi.org/10.1103/PhysRevLett.119.060601
© 2017 American Physical Society