一维简并费米气体的弛豫
Relaxation of the degenerate one-dimensional Fermi gas
摘要：
我们研究了一维自旋为1/2的费米子系统在远低于费米能的温度下如何接近热平衡。费米子之间的相互作用被假设为很弱，并且在微扰理论中得到了解释。在没有外部磁场的情况下，自旋简并强烈影响费米气体的弛豫。对于足够短程的相互作用，弛豫速率与温度成线性比例。针对系统接近平衡时的情形，我们将碰撞积分线性化，得到了松弛问题的精确解。我们讨论了我们的结果的应用，一维费米气体的输运系数的评估。
英文摘要：
We study how a system of one-dimensional spin-1/2 fermions at temperatures well below the Fermi energy approaches thermal equilibrium. The interactions between fermions are assumed to be weak and are accounted for within the perturbation theory. In the absence of an external magnetic field, spin degeneracy strongly affects relaxation of the Fermi gas. For sufficiently short-range interactions, the rate of relaxation scales linearly with temperature. Focusing on the case of the system near equilibrium, we linearize the collision integral and find exact solution of the resulting relaxation problem. We discuss the application of our results to the evaluation of the transport coefficients of the one-dimensional Fermi gas.
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