Journal
PHYSICAL REVIEW X
Volume 7, Issue 4, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevX.7.041001
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Funding
- Aarhus University Research Foundation
- U.S. National Science Foundation [PHY-1607221]
- Office of Naval Research Grant [N00014-12-1-0400]
- Danish Council for Independent Research (Sapere Aude)
- Humboldt Foundation
- Direct For Mathematical & Physical Scien
- Division Of Physics [1607221] Funding Source: National Science Foundation
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We show that the dynamics of particles in a one-dimensional harmonic trap with hard-core interactions can be solvable for certain arrangements of unequal masses. For any number of particles, there exist two families of unequal mass particles that have integrable dynamics, and there are additional exceptional cases for three, four, and five particles. The integrable mass families are classified by Coxeterre flection groups and the corresponding solutions are Bethe-ansatz-like superpositions of hyperspherical harmonics in the relative hyperangular coordinates that are then restricted to sectors of fixed particle order. We also provide evidence for superintegrability of these Coxeter mass families and conjecture maximal superintegrability.
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