Correlation effects in quantum dots and wires

在这个项目中，我们研究了（准）一维量子线和“零”维量子点中的相关效应，特别关注这些系统在线性响应状态下的输运性质和单粒子光谱性质。我们已经成功地将截断方案应用于直接实验相关的问题（“相位失效难题”和多层点的充电，通过相关量子点的约瑟夫森电流）。静态近似只能在非弹性过程无关的情况下使用（例如温度T = 0电导）。因此，我们扩展了截断方案，并保持了两粒子顶点的频率依赖性，从而在单粒子不可约泛函RG中导致频率依赖性的自能。我们应用该方案研究了单杂质Anderson模型（在适当的参数域中以自旋涨落为主）和相互作用谐振能级模型（以电荷涨落为主）。我们讨论了这个方案的优缺点。我们将尝试改进后者（高阶修正）。接下来，我们将使用频率相关的近似来研究更复杂的量子点系统，显示出由近藤效应和其他相互作用（如RKKY）的相互作用所主导的物理。我们将扩展频率相关方案来研究量子线。一个有趣的问题是体积和边界卢廷格液体物理之间的交叉。最后，我们将使用频率依赖方案来研究与玻色子耦合的费米子系统（例如，与声子耦合的局部电子能级）。

In this project we investigate correlation effects in (quasi) one-dimensional quantum wires and in “zero”-dimensional quantum dots with a particular focus on the transport properties of such systems in the linear response regime and singleparticle spectral properties. We have successfully applied a truncation scheme leading to a static self-energy to problems of direct experimental relevance (“phase lapse puzzle” and charging of multi-level dots, Josephson current through correlated quantum dot). The static approximation can only be used in situation in which inelastic processes are irrelevant (e.g. temperatur T = 0 conductance). We thus extended the truncation scheme and kept the frequency dependence of the two-particle vertex which within the one-particle irreducible functional RG leads to a frequency dependent self-energy. We applied this scheme to study the singleimpurity Anderson model (in the appropriate parameter regime dominated by spin fluctuations) and the interacting resonant level model (dominated by charge fluctuations). We discussed the merits and drawbacks of this scheme. We will try to improve on the latter (higher-order corrections). Next we will use the frequency dependent approximation to investigate more complex systems of quantum dots showing a physics which is dominated by the interplay of the Kondo effect and other interactions (such as the RKKY). We will extend the frequency dependent scheme to study quantum wires. An interesting question is the crossover between bulk and boundary Luttinger liquid physics. Finally, we will use the frequency dependent scheme to study fermionic systems coupled to bosons (e.g. local electronic levels coupled to phonons.)