Harmonically Confined Particles with Long-Range Repulsive Interactions

We study an interacting system of N 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 ∝∑i≠jN|xi−xj|−k (with k>−2) of their mutual distance. This is a generalizatio...

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Bibliographic Details
Published in:Physical review letters 2019-09, Vol.123 (10), p.100603, Article 100603
Main Authors: Agarwal, S., Dhar, A., Kulkarni, M., Kundu, A., Majumdar, S. N., Mukamel, D., Schehr, G.
Format: Article
Language:English
Subjects:
Dependence
Physics
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Summary:We study an interacting system of N 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 ∝∑i≠jN|xi−xj|−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→0+), and the Calogero-Moser model (k=2). Because of 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
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.123.100603