论文标题
在存在软泊松障碍物的情况下，在一维非互动的玻色气中的Bose-Einstein凝结上
On Bose-Einstein condensation in one-dimensional noninteracting Bose gases in the presence of soft Poisson obstacles
论文作者
论文摘要
我们在$ \ Mathbb r $上的一维非相互作用的bose气体中研究了Bose-Einstein凝结（BEC），具有单点电位，具有单点电位，这些电位是非负值，紧凑的，有限的且有限的可测量函数，可在盛大的良好的良好的温度下在热力学限制的正温度下。对于比关键粒子大的粒子密度，我们证明了以下内容：选择足够大的随机电位的固定强度时，只有宏观占据宏观占据的固定强度时，发生固定强度。如果泊松随机电势的强度在某种意义上但任意慢慢地收敛到无穷大，那么这种BEC发生在概率和$ r $ th的概率中，$ r \ ge 1 $。此外，在任何固定强度的泊松随机电势中，也可以通过允许足够多的一粒子状态宏观地占据，从而获得任意高的I G-BEC的可能性。
We study Bose-Einstein condensation (BEC) in one-dimensional noninteracting Bose gases in Poisson random potentials on $\mathbb R$ with single-site potentials that are nonnegative, compactly supported, and bounded measurable functions in the grand-canonical ensemble at positive temperatures in the thermodynamic limit. For particle densities that are larger than a critical one, we prove the following: With arbitrarily high probability when choosing the fixed strength of the random potential sufficiently large, BEC where only the ground state is macroscopically occupied occurs. If the strength of the Poisson random potential converges to infinity in a certain sense but arbitrarily slowly, then this kind of BEC occurs in probability and in the $r$th mean, $r \ge 1$. Furthermore, in Poisson random potentials of any fixed strength an arbitrarily high probability for type-I g-BEC is also obtained by allowing sufficiently many one-particle states to be macroscopically occupied.
