Abstract
We study an interacting system of classical particles on a line at thermal equilibrium. The particles are confined by a harmonic trap and repel each other via pairwise interaction potential that behaves as a power law (with ) of their mutual distance. This is a generalization of the well-known cases of the one-component plasma (), Dyson’s log gas (), and the Calogero-Moser model (). Because of the competition between harmonic confinement and pairwise repulsion, the particles spread over a finite region of space for all . We compute exactly the average density profile for large for all and show that while it is independent of temperature for sufficiently low temperature, it has a rich and nontrivial dependence on with distinct behavior for , and .
- Received 11 June 2019
DOI:https://doi.org/10.1103/PhysRevLett.123.100603
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