均匀相互作用玻色子系统中相变的证明
Proof of phase transition in homogeneous systems of interacting bosons
摘要：
利用Feynman和Kac的严格路径积分形式，证明了伦敦80年前提出的猜想：在液氦超流转变过程中发生了玻色-爱因斯坦凝聚（BEC）.首先证明在足够低的温度下系统中出现宏观置换环，然后证明这意味着BEC。我们还发现，在零温度的限制下，无限循环覆盖整个系统，而BEC保持部分。对于静止的玻色凝聚流体，我们定义了一个宏观波函数。通过1/2自旋和硬核玻色子的等价性，该方法扩展到格点模型。我们表明，在足够低的温度下，自旋1/2轴向各向异性海森堡模型，包括各向同性铁磁和反铁磁和XY模型，进行磁有序。
英文摘要：
Using the rigorous path integral formalism of Feynman and Kac we prove London's eighty years old conjecture that during the superfluid transition in liquid helium Bose-Einstein condensation (BEC) takes place. The result is obtained by proving first that at low enough temperatures macroscopic permutation cycles appear in the system, and then showing that this implies BEC. We find also that in the limit of zero temperature the infinite cycles cover the whole system, while BEC remains partial. For the Bose-condensed fluid at rest we define a macroscopic wave function. Via the equivalence of 1/2 spins and hard-core bosons the method extends to lattice models. We show that at low enough temperatures the spin-1/2 axially anisotropic Heisenberg models, including the isotropic ferro- and antiferromagnet and the XY model, undergo magnetic ordering.
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