论文标题
谭的关系分解为有损的一维玻璃气体
Breakdown of Tan's relation in lossy one-dimensional Bose gases
论文作者
论文摘要
在具有接触率的量子气体中，原子的动量分布通常衰减为$ \ sim 1/| p |^4 $在大动量$ p $下。谭的关系将$ 1/| p |^4 $尾巴的幅度连接到与气体耦合常数或散射长度相对于能量的绝热导数。这里表明，对于特殊的固定状态类别的一维玻色气体中的关系分解。这些状态由于系统中的无限量数量而存在，它们的特征是速度分布本身降低为$ 1/| p |^4 $。在动量分布中，速度尾巴增加了通常的棕褐色接触术语。值得注意的是，在实验中无处不在的原子损失确实会产生这种特殊的状态。速度分布的尾巴的发展起源于每次损失事件后立即发挥作用的幽灵奇异性。讨论了这种现象的任意相互作用强度，并且在两个无限和弱排斥的渐近方案中的确切计算得到了支持。
In quantum gases with contact repulsion, the distribution of momenta of the atoms typically decays as $\sim 1/|p|^4$ at large momentum $p$. Tan's relation connects the amplitude of that $1/|p|^4$ tail to the adiabatic derivative of the energy with respect to the gas' coupling constant or scattering length. Here it is shown that the relation breaks down in the one-dimensional Bose gas with contact repulsion, for a peculiar class of stationary states. These states exist thanks to the infinite number of conserved quantities in the system, and they are characterized by a rapidity distribution which itself decreases as $1/|p|^4$. In the momentum distribution, that rapidity tail adds to the usual Tan contact term. Remarkably, atom losses, which are ubiquitous in experiments, do produce such peculiar states. The development of the tail of the rapidity distribution originates from the ghost singularity of the wavefunction immediately after each loss event. This phenomenon is discussed for arbitrary interaction strengths, and it is supported by exact calculations in the two asymptotic regimes of infinite and weak repulsion.
