哈密顿平均场模型中的核晕分布
Core-halo distribution in the Hamiltonian Mean-Field Model
摘要：
我们研究了一个具有长程相互作用的范式系统：哈密顿平均场模型（HMF）。结果表明，在热力学极限下，该模型不会松弛到通常的平衡麦克斯韦-玻尔兹曼分布。相反，最终的定态有一个特殊的核心晕结构。在热力学极限下，HMF既不是遍历的，也不是混合的。然而，我们发现，利用哈密顿系统的动力学性质，它是可能的定量预测自旋分布和速度分布函数在最终的定态，没有任何可调参数。我们还表明，HMF经历了一个非平衡的一级相变之间的顺磁和铁磁状态。
英文摘要：
We study a paradigmatic system with long-range interactions: the Hamiltonian Mean-Field Model (HMF). It is shown that in the thermodynamic limit this model does not relax to the usual equilibrium Maxwell-Boltzmann distribution. Instead, the final stationary state has a peculiar core-halo structure. In the thermodynamic limit, HMF is neither ergodic nor mixing. Nevertheless, we find that using dynamical properties of Hamiltonian systems, it is possible to quantitatively predict both the spin distribution and the velocity distribution functions in the final stationary state, without any adjustable parameters. We also show that HMF undergoes a non-equilibrium first-order phase transition between paramagnetic and ferromagnetic states.
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