论文标题
回顾一种在所有密度研究的简化方法
Review of a Simplified Approach to study the Bose gas at all densities
论文作者
论文摘要
在本文中，我们将回顾埃里克·A·卡伦（Eric A.简化的方法产生了有效的单粒子方程系列，该方程在低密度和高密度下捕获了叶气体的某些非平凡的物理特性，甚至在中间密度下的某些行为。特别是，简化的方法再现了Bogolyubov对基态能量和低密度下的凝结分数的估计，以及高密度下能量的平均田间估计值。我们还将讨论出现在具有液体样性质的中间密度的阶段。可以分析地研究简化方法中最简单的方程式，我们将回顾一些结果。到目前为止，其他人只能接受数值分析，我们将讨论几个数值结果。首先，我们将审查Bose气体上的一些结果和猜想，然后引入简化的方法及其从Bose气体引入。然后，我们将讨论简化方法的预测，并将这些预测与有关玻色气体的结果和猜想进行比较。最后，我们将讨论一些关于简化方法的开放问题。
In this paper, we will review the results obtained thus far by Eric A. Carlen, Elliott H. Lieb and me on a Simplified Approach to the Bose gas. The Simplified Approach yields a family of effective one-particle equations, which capture some non-trivial physical properties of the Bose gas at both low and high densities, and even some of the behavior at intermediate densities. In particular, the Simplified Approach reproduces Bogolyubov's estimates for the ground state energy and condensate fraction at low density, as well as the mean-field estimate for the energy at high densities. We will also discuss a phase that appears at intermediate densities with liquid-like properties. The simplest of the effective equations in the Simplified Approach can be studied analytically, and we will review several results about it; the others are so far only amenable to numerical analysis, and we will discuss several numerical results. We will start by reviewing some results and conjectures on the Bose gas, and then introduce the Simplified Approach and its derivation from the Bose gas. We will then discuss the predictions of the Simplified Approach and compare these to results and conjectures about the Bose gas. Finally, we will discuss a few open problems about the Simplified Approach.
