In this work, we analyze the corrections obtained on a homogeneous one-dimensional Bose gas within the high densities limit by means of the non-regular representation of quantum mechanics introduced by the polymer quantization scheme. Thus, starting from the Bogoliubov formalism, we analyze the ground expectation value of the polymer momentum operator in terms of semiclassical states in order to obtain an analytic expression for the ground state energy of the N-body system, which allows us to solve the pathological behavior commonly associated with the one-dimensional Bose–Einstein condensation through the introduction of finite size effects characterized by the contribution of the polymer corrections. We also discuss the speed of sound in our polymer version of the Bose gas and the corresponding relative shift induced by the introduction of a minimum length parameter. Finally, we investigate the emergent superfluid behavior in our polymer model by implementing an appropriate Landau’s criterion. In this case, we are able to consequently analyze the changes in the critical velocity which defines the limit between the superfluid-condensate regions, thus deducing that the polymer length acts as a kind of pseudo-potential which induces a dissipationless flow associated with the superfluid phase even in the absence of self-interactions.

中文翻译：

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聚合物量子力学中的超流体

在这项工作中，我们通过聚合物量子化方案引入的量子力学的非常规表示，分析了在高密度极限内对均匀一维玻色气体获得的校正。因此，我们从 Bogoliubov 形式出发，分析聚合物动量算子的半经典态的基期望值，以获得 N 体系​​统基态能量的解析表达式，从而解决了病态的问题。通过引入以聚合物校正的贡献为特征的有限尺寸效应，通常与一维玻色-爱因斯坦凝聚相关的行为。我们还讨论了我们的聚合物版本的 Bose 气体中的声速以及由引入最小长度参数引起的相应相对位移。最后，我们通过实施适当的朗道准则来研究聚合物模型中出现的超流体行为。在这种情况下，我们因此能够分析临界速度的变化，该临界速度定义了超流体-冷凝区域之间的界限，从而推断出聚合物长度作为一种赝势，导致与超流体相关的无耗散流动即使在没有自我交互的情况下也能相。