For Riesz gases confined by a hard wall, complete confinement to the wall occurs exactly in the strongly long-ranged regime s∈(d-3,d-2], with an explicit critical wall position; in the weakly long-ranged regime s∈(d-2,d) it never occurs.
Minimizers for Coulomb gases constrained to a halfspace
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abstract
We consider a family of optimization problems, based on a mean-field description of particles interacting through Coulomb forces in a quadratic trap. In addition, the particles are constrained to lie in a halfspace and we are interested in the way the particle distribution changes as the halfspace varies. In particular, we can prove the existence of a phase transition, thereby settling a recent conjecture by Byun, Forrester, Majumdar and Schehr.
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Confinement transitions in half-space constrained Riesz gases
For Riesz gases confined by a hard wall, complete confinement to the wall occurs exactly in the strongly long-ranged regime s∈(d-3,d-2], with an explicit critical wall position; in the weakly long-ranged regime s∈(d-2,d) it never occurs.