论文标题
用于球形约束谐波模型的广义吉布斯合奏
Generalised Gibbs Ensemble for spherically constrained harmonic models
论文作者
论文摘要
我们构建和分析计算可集成软诺伊曼模型的广义吉布斯集成分区功能。这是经典粒子的模型，在初始条件下，在$ n $尺寸的球体上平均被限制移动，并感受到各向异性谐波电位的效果。我们在（热力学）$ n \ rightarrow \ infty $限制中得出所有相关的平均静态可观察物。我们将它们与他们的长期动态平均值进行比较，在非平凡相图的所有阶段中找到了良好的一致性，这些相图由初始条件的特征以及在瞬时淬灭中注入或提取的能量的量确定。我们讨论了我们结果的含义，即严格施加球形约束的适当的诺伊曼模型。
We build and analytically calculate the Generalised Gibbs Ensemble partition function of the integrable Soft Neumann Model. This is the model of a classical particle which is constrained to move, on average over the initial conditions, on an $N$ dimensional sphere, and feels the effect of anisotropic harmonic potentials. We derive all relevant averaged static observables in the (thermodynamic) $N\rightarrow\infty$ limit. We compare them to their long-term dynamic averages finding excellent agreement in all phases of a non-trivial phase diagram determined by the characteristics of the initial conditions and the amount of energy injected or extracted in an instantaneous quench. We discuss the implications of our results for the proper Neumann model in which the spherical constraint is imposed strictly.
