We develop a variational theory for a dipolar condensate in an elongated (cigar shaped) confinement potential. Our formulation provides an effective one-dimensional extended meanfield theory for the ground state and its collective excitations. We apply our theory to investigate the properties of rotons in the system comparing the variational treatment to a full numerical solution. We consider the effect of quantum fluctuations on the scattering length at which the roton excitation softens to zero energy.

中文翻译：

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细长偶极凝聚态基态和集体激发的变分理论

我们为细长（雪茄形）限制势中的偶极冷凝物开发了变分理论。我们的公式为基态及其集体激发提供了有效的一维扩展平均场理论。我们应用我们的理论来研究系统中旋转子的特性，将变分处理与完整的数值解进行比较。我们考虑了量子涨落对旋转子激发软化到零能量的散射长度的影响。