We investigate the effect of losses on an interacting quantum gas. We show that, for gases in dimensions higher than one, assuming together a vanishing correlation time of the reservoir where dissipation occurs, and contact interactions lead to a divergence of the energy increase rate. This divergence is a combined effect of the contact interactions, which impart arbitrary large momenta to the atoms, and the infinite energy width of the reservoir associated with its vanishing correlation time. We show how the divergence is regularized when taking into account the finite energy width of the reservoir, and, for a large energy width, we give an expression for the energy increase rate that involves the contact parameter. We then consider the specific case of a weakly interacting Bose-Einstein condensate, that we describe using the Bogoliubov theory. Assuming slow losses so that the gas is at any time described by a thermal equilibrium, we compute the time evolution of the temperature of the gas. Using a Bogoliubov analysis, we also consider the case where the regularization of the divergence is due to the finite range of the interaction between atoms.

中文翻译：

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相互作用量子气体的损失：紫外线发散及其正则化

我们研究了损耗对相互作用量子气体的影响。我们表明，对于维度高于 1 的气体，一起假设发生耗散的储层的相关时间消失，并且接触相互作用导致能量增加率的发散。这种发散是接触相互作用的综合效应，它赋予原子任意大的动量，以及与其消失的相关时间相关的储层的无限能量宽度。我们展示了在考虑到储层的有限能量宽度时发散是如何正则化的，并且对于大的能量宽度，我们给出了涉及接触参数的能量增加率的表达式。然后，我们考虑使用 Bogoliubov 理论描述的弱相互作用玻色-爱因斯坦凝聚的具体情况。假设缓慢损失使得气体在任何时间都由热平衡描述，我们计算气体温度的时间演变。使用 Bogoliubov 分析，我们还考虑了散度的正则化是由于原子之间相互作用的有限范围的情况。