论文标题
弱相互作用的bose气体的导热率
Thermal conductivity of a weakly interacting Bose gas in quasi-one-dimension
论文作者
论文摘要
在一个维度上，对于量子积分系统，传输系数通常会发散，例如具有两体接触相互作用的bose气体。但是，当通过将玻色子限制在紧密的物质波导中实现一维系统时，有效的三体相互作用不可避免地会导致破坏整合性。这一事实促使我们研究了两体和三体相互作用的一个维度的玻色气体的导热率。特别是，我们通过总结所有在扰动中天气较高的贡献，但由于捏合奇异性而在零频率的极限上相当，将库博公式完全评估为扰动的最低顺序。因此，得出了顶点函数的自洽方程式，表明准二比中的热导率由三体相互作用而不是两体相互作用主导。此外，弱耦合极限中产生的热导率证明与基于量子玻尔兹曼方程计算的电导率相同，其温度依赖性是数值确定的。
Transport coefficients are typically divergent for quantum integrable systems in one dimension, such as a Bose gas with a two-body contact interaction. However, when a one-dimensional system is realized by confining bosons into a tight matter waveguide, an effective three-body interaction inevitably arises as leading perturbation to break the integrability. This fact motivates us to study the thermal conductivity of a Bose gas in one dimension with both two-body and three-body interactions. In particular, we evaluate the Kubo formula exactly to the lowest order in perturbation by summing up all contributions that are naively higher orders in perturbation but become comparable in the zero-frequency limit due to the pinch singularity. Consequently, a self-consistent equation for a vertex function is derived, showing that the thermal conductivity in quasi-one-dimension is dominated by the three-body interaction rather than the two-body interaction. Furthermore, the resulting thermal conductivity in the weak-coupling limit proves to be identical to that computed based on the quantum Boltzmann equation and its temperature dependence is numerically determined.
