一维谐振阱中不等质量硬核粒子的可积族
Integrable families of hard-core particles with unequal masses in a one-dimensional harmonic trap
摘要：
我们表明，在一维谐波陷阱与硬核相互作用的粒子的动力学可以解决某些安排的不平等的质量。对于任何数量的粒子，存在两个具有可积动力学的不等质量粒子族，并且存在三个、四个和五个粒子的额外例外情况。可积的质量族被分类的Coxeter反射群和相应的解决方案是Bethe ansatz的超球谐函数的叠加在相对超角坐标，然后被限制到固定的粒子顺序的部门。我们还提供了这些Coxeter质量家庭的超可积性和猜想最大超可积性的证据。
英文摘要：
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 Coxeter reflection 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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