标题： 普朗克尺度在捕获的玻色-爱因斯坦凝聚体中的声速 显示英文标题

标题： Planck Scale Induced Speed of Sound in a Trapped Bose-Einstein Condensate

摘要： 在本工作中，我们分析了由异常色散关系引起的修正，该关系在多个量子引力模型中被提出，对弱相互作用玻色-爱因斯坦凝聚体中声速的影响，该凝聚体被束缚在形式为$V(r)\sim r^{2}$的势场中。我们表明，相应的基态能量以及由此产生的声速相对于通常情况存在修正，这些修正可用于探索与凝聚体相关的重要性质对普朗克尺度效应的敏感性。事实上，我们强调，在某些条件下，这种宏观物体可能比其组成部分对普朗克尺度的表现更加敏感。此外，我们证明，包括势场和多体贡献在内的因素，相比均匀系统，提高了对普朗克尺度信号的敏感性。 显示英文摘要

摘要： In the present work, we analyze the corrections caused by an anomalous dispersion relation, suggested in several quantum gravity models, upon the speed of sound in a weakly interacting Bose--Einstein Condensate, trapped in a potential of the form $V(r)\sim r^{2}$. We show that the corresponding ground state energy and consequently, the associated speed of sound, present corrections respect to the usual case, which may be used to explore the sensitivity to Planck--scale effects on these relevant properties associated with the condensate. Indeed, we stress that this type of macroscopic bodies may be more sensitive, under certain conditions, to Planck--scale manifestations than its constituents. In addition, we prove that the inclusion of a trapping potential, together with many--body contributions, improves the sensitivity to Planck--scale signals, compared to the homogeneous system.