量子可积模型中的功能独立守恒律
Functionally independent conservations laws in a quantum integrable model
AI总结：
本文提出一个量子可积模型，通过展示其功能独立守恒律的数量与自由度N的关系，揭示了可积性与自由度之间的联系。
摘要：
我们研究了一个最近提出的量子可积模型，该模型定义在具有N个站点的晶格上，每个站点由费米子或玻色子占据，作为众所周知的自旋1/2 Gaudin模型的近亲。该模型有2N个任意参数，与相互作用类型参数x线性相关，并且可以精确求解。它有N个已知的守恒量，与x线性相关。我们进一步展示了具有更高费米子含量的守恒量，这些守恒量在已知守恒律中是线性无关的。我们的主要结果是，尽管存在这些更高守恒律，该模型仅有N个功能独立的守恒律。因此我们提出，N可以被视为自由度的数量，类似于经典可积性的定义。
英文摘要：
We study a recently proposed quantum integrable model defined on a lattice with N sites, with Fermions or Bosons populating each site, as a close relative of the well known spin-1/2 Gaudin model. This model has 2N arbitrary parameters, a linear dependence on an interaction type parameter x, and can be solved exactly. It has N known constants of motion that are linear in x. We display further constants of motion with higher Fermion content, that are are linearly independent of the known conservation laws. Our main result is that despite the existence of these higher conservation laws, the model has only N functionally independent conservation laws. Therefore we propose that N can be viewed as the number of degrees of freedom, in parallel to the classical definition of integrability.
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