An analysis of open quantum systems with interactions and its application to the theory of electron conduction

我们通过多电子散射本征态的精确解研究了相互作用的开放量子点系统。首先，我们研究了由双引线相互作用共振能级模型描述的开放量子点系统的电子输运性质。我们构造的准确的多电子散射态并不是已知的Bethe本征态的形式，也就是说，在散射过程中入射平面波的波数集是不守恒的，并且在散射之后出现了多体约束态。通过将散射态应用于Landauer公式的推广，我们计算了在有限偏压下通过量子点的平均电流。通过考虑二体束缚态得到的电流-电压特性与几个已知结果定性地吻合。接下来，我们从理论上提出了通过双引线Anderson模型描述的开放量子点系统产生纠缠。我们准确地得到了一条引线的非纠缠入射态与另一条引线的出射自旋单重态之间的跃迁速率。我们发现，在共隧道散射过程中，只有自旋-单重态才能传输。

We studied interacting open quantum dot systems through an exact solution of many-electron scattering eigenstates. First, we investigated the electron transport property of an open quantum dot system described by the two-lead interacting resonant-level model. The exact many-electron scattering states that we constructed are not in the form of the known Bethe eigenstates in the sense that the wave-number set of the incident plane wave is not conserved during the scattering and many-body bound states appear after the scattering. By applying the scattering states to an extension of the Landauer formula, we calculated the average electric current through the quantum dot under a finite bias voltage. The current-voltage characteristics that we obtained by taking the two-body bound state into account qualitatively agrees with several known results. Next, we theoretically proposed entanglement generation through an open quantum dot system described by the two-lead Anderson model. We exactly obtained the transition rate between the non-entangled incident state in one lead and the outgoing spin-singlet state in the other lead. We found that only the spin-singlet state can transmit in a cotunneling scattering process.