Exact Extremal Statistics in the Classical 1D Coulomb Gas

Abhishek Dhar, Anupam Kundu, Satya N. Majumdar, Sanjib Sabhapandit, and Grégory Schehr
Phys. Rev. Lett. 119, 060601 – Published 8 August 2017
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Abstract

We consider a one-dimensional classical Coulomb gas of N-like charges in a harmonic potential—also known as the one-dimensional one-component plasma. We compute, analytically, the probability distribution of the position xmax of the rightmost charge in the limit of large N. We show that the typical fluctuations of xmax around its mean are described by a nontrivial scaling function, with asymmetric tails. This distribution is different from the Tracy-Widom distribution of xmax for Dyson’s log gas. We also compute the large deviation functions of xmax explicitly and show that the system exhibits a third-order phase transition, as in the log gas. Our theoretical predictions are verified numerically.

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  • Received 28 April 2017

DOI:https://doi.org/10.1103/PhysRevLett.119.060601

© 2017 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsGeneral Physics

Authors & Affiliations

Abhishek Dhar1, Anupam Kundu1, Satya N. Majumdar2, Sanjib Sabhapandit3, and Grégory Schehr2

  • 1International Centre for Theoretical Sciences, TIFR, Bangalore 560089, India
  • 2LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
  • 3Raman Research Institute, Bangalore 560080, India

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Issue

Vol. 119, Iss. 6 — 11 August 2017

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