论文标题
原子损失对一维玻色气体速度分布的影响
The effect of atom losses on the distribution of rapidities in the one-dimensional Bose gas
论文作者
论文摘要
从理论上讲，我们研究原子损失在具有排斥性接触相互作用的一维（1D）玻色气体中，这是一个著名的量子整合系统，也称为Lieb-Liniger Gas。考虑了K体损失的通用情况（K = 1,2,3，...）。我们假设损耗率远小于系统的固有松弛率，因此在任何时候，系统的速度分布都会捕获（或等效地是由广义的Gibbs集合）捕获的。我们给出了管理快速分布的时间演变的方程式，并提出了一个通用的数值程序来解决它。在消失排斥的渐近方案中 - 气体的表现像理想的玻璃气 - 和硬核排斥 - 我们得出了分析公式。在后一种情况下，我们的分析结果表明，损失以非平凡的方式影响速度分布，而速度分布的时间导数在速度空间中既非线性和非本地”。
We theoretically investigate the effects of atom losses in the one-dimensional (1D) Bose gas with repulsive contact interactions, a famous quantum integrable system also known as the Lieb-Liniger gas. The generic case of K-body losses (K = 1,2,3,...) is considered. We assume that the loss rate is much smaller than the rate of intrinsic relaxation of the system, so that at any time the state of the system is captured by its rapidity distribution (or, equivalently, by a Generalized Gibbs Ensemble). We give the equation governing the time evolution of the rapidity distribution and we propose a general numerical procedure to solve it. In the asymptotic regimes of vanishing repulsion -- where the gas behaves like an ideal Bose gas -- and hard-core repulsion -- where the gas is mapped to a non-interacting Fermi gas -- we derive analytic formulas. In the latter case, our analytic result shows that losses affect the rapidity distribution in a non-trivial way, the time derivative of the rapidity distribution being both non-linear and non-local in rapidity space.
