一维均匀玻色-爱因斯坦凝聚体在Bogoliubov区域的聚合物量子化
Polymer quantization in the Bogoliubov's regime for a homogeneous one-dimensional Bose-Einstein condensate
摘要：
在本报告中，我们分析了聚合物量子化对均匀一维玻色-爱因斯坦凝聚体基态的最终影响。我们得到了相应的N体系统的基态能量，因此，相应的声速，使我们能够探索系统的灵敏度所造成的聚合物量子化的校正。由于聚合物量子化引起的校正可以改善稠密系统连同相应的一维散射长度的小值。然而，由于系统的有限尺寸效应，这些校正仍然受到限制。聚合物的长度尺度的系统的基态能量的属性的贡献，使我们能够探索，作为一个第一近似值，当Bogoliubov的形式主义是有效的，这个多体系统的灵敏度所造成的空间离散性的聚合物量子化的痕迹。
英文摘要：
In the present report we analyze the eventual modifications caused by the polymer quantization upon the ground state of a homogeneous one-dimensional Bose-Einstein condensate. We obtain the ground state energy of the corresponding N-body system and, consequently, the corresponding speed of sound, allowing us to explore the sensitivity of the system to corrections caused by the polymer quantization. The corrections arising from the polymer quantization can be improved for dense systems together with small values of the corresponding one-dimensional scattering length. However, these corrections remain constrained due to finite size effects of the system. The contributions of the polymer length scale to the properties of the ground state energy of the system allow us to explore, as a first approximation and when the Bogoliubov's formalism is valid, the sensitivity of this many-body system to traces caused by the discreteness of space suggested by the polymer quantization.
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