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arXiv 1409.4277cond-mat.quant-gascond-mat.stat-mechhep-th
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受压下的二维玻色-爱因斯坦凝聚体

Two-dimensional Bose-Einstein condensate under pressure

Wonyoung Cho, Sang-Woo Kim, Jeong-Hyuck Park

备注：
17 pages, 4 figures; version expanded, To appear in New Journal of Physics
发表信息：
New J. Phys. 17 (2015) 013038
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摘要：

避开Mermin-Wagner-Hohenberg不去定理，严格地重新审视了被限制在正方形盒子中的理想玻色气体，我们探讨了二维空间中的离散相变。通过分析和数值方法，我们验证了热力学不稳定性出现，如果粒子的数量是足够大的，但仍然很大：特别是$N\geq 35131$。这种不稳定性意味着气体的等压线在温度-体积平面上的不稳定性，具有过冷和过热现象。然后，玻色-爱因斯坦凝聚可以从绝对零度持续到过热温度。在定压条件下，不一定取大的$N$极限，凝聚在动量空间和位置空间都离散地发生。我们的结果适用于谐波陷阱。我们断言实验观察到的谐波囚禁原子气体的玻色-爱因斯坦凝聚是一个一级相变，它涉及在陷阱中心的密度的离散变化。

英文摘要：

Evading the Mermin-Wagner-Hohenberg no-go theorem and revisiting with rigor the ideal Bose gas confined in a square box, we explore a discrete phase transition in two spatial dimensions. Through both analytic and numerical methods we verify that thermodynamic instability emerges if the number of particles is sufficiently yet finitely large: specifically $N\geq 35131$. The instability implies that the isobar of the gas zigzags on the temperature-volume plane, featuring supercooling and superheating phenomena. The Bose-Einstein condensation then can persist from absolute zero to the superheating temperature. Without necessarily taking the large $N$ limit, under constant pressure condition, the condensation takes place discretely both in the momentum and in the position spaces. Our result is applicable to a harmonic trap. We assert that experimentally observed Bose-Einstein condensations of harmonically trapped atomic gases are a first-order phase transition which involves a discrete change of the density at the center of the trap.

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