Visiting Fellowship for Prof. Alexei Tsvelik

1.普遍的观点认为，铜氧化物超导体在低掺杂状态下与传统的BCS超导体有着本质的不同。这种差异是揭示在一个宽的温度范围以上Tc，其中的序参数amplitudeis定义良好，但（全球）秩序尚未出现由于相位波动的存在。有大量的实验证据支持铜氧化物中强的相位波动，例如从抗磁化率和Tc以上的能斯特效应的测量中得到的。在小的掺杂量下，比热的跃变大大减小，这表明超导转变更接近于二维Berezinskiii-Kosterlitz-无相变。最近的光电子能谱实验揭示了高Tc超导体正常相的电子性质的有趣的新信息。为了解释这些数据，已经提出了一些理论方法。一种可能的方法是从超导体开始，然后考虑热涨落，这将引起超导序参量相位的涨落。一个重要的问题是这些涨落是如何在角分辨光电子能谱实验测量的单粒子谱函数中表现出来的，从实验的角度来看，特别令人感兴趣的问题是费米口袋是否自然地出现在这样的模型中.长期以来，人们已经知道，一维量子流体的低能性质可以通过称为Luttinger液体（LL）的有效流体动力学理论来描述。LL方法是基于线性化的低洼部分的spectrumand导致从相互作用的费米子或玻色子模型的线性流体力学理论，这是一个非相互作用的谐波emisatormodes的集合的地图。在过去的30年中，LL方法已被应用于许多一维问题，如准一维量子磁体，量子线，碳纳米管，有机导体，超冷原子气体，取得了巨大的成功。重要的是，LL方法允许计算响应函数的大的时间和空间渐近性，例如动力学结构因子或单粒子谱函数，它们分别可由非弹性中子散射和光电子实验直接访问。用这种方法得到的动力学响应函数的一个特征是幂律阈值奇异性。最近人们意识到，这些奇异性实际上是由LL方法中忽略的谱的非线性所修改的。对于基态是由一个单一的费米子或玻色子的情况下，存在一个映射的thresholdsingularity的问题，一个有效的X射线边缘问题的移动的核心孔。后者是可解的，并允许在动态响应函数的奇异性的确定。对于应用，如库仑阻力和动量分辨隧道的电子之间的量子线。对于这些应用，了解自旋电子模型的动力学响应中的阈值奇异性结构是很有用的，在这里，由于低能时的自旋-电荷分离，人们可以期望比单粒子情况下更丰富的结构.

1. There is a popular viewpoint that the cuprate superconductors in their underdoped regime are fundamentally different from conventionalBCS ones. This difference is revealed in the existence of a wide temperature range above Tc, where the order parameter amplitudeis well defined but (global) order has not yet emerged due to phase fluctuations. There is ample experimental evidence in favour of strong phase fluctuations in the cuprates, derived e.g. from measurements ofthe diamagnetic susceptibility and the Nernst effect above Tc. The jump in the specific heat is strongly reduced atsmall doping, which is an indication that the superconducting transition becomes closer to a two dimensionalBerezinskii-Kosterlitz-Thouless transition. Recent photoemission experiments have revealed interesting new information on the electronic properties of the normal phase of high-Tc superconductors. A number of theoretical approaches have been proposed in order to interpret the data. One possible approach is to start with a superconductor and then take thermal fluctuations into account.These will induce fluctuations in the phase of the superconducting order parameter. An important question is how these fluctuationsmanifest themselves in the single particle spectral function measured by angle resolved photoemission experiments.Of particular interest in view of the experiments is the question whether Fermi pockets naturally emerge in such a model.2. It has been known for a long time that low-energy properties of one dimensional quantum fluids can be described by means of aneffective hydrodynamic theory known as Luttinger liquid (LL). The LL approach is based on linearizing the low-lying part of the spectrumand leads to a map from interacting fermion or boson models to a linear hydrodynamic theory, which is a collection of non-interacting harmonic oscillatormodes. Over the last 30 years The LL approach has been applied to a host of one dimensional problems such as quasi one dimensional quantummagnets, quantum wires, carbon nanotubes, organic conductors, ultra-cold atomic gases with enormous success. Importantly, the LL approach allows the calculation of the large time and space asymptotics of response functions such as the dynamical structure factor or the single particle spectral function that are directly accessible by inelastic neutron scattering and photoemission experiments respectively. A characteristic feature of the dynamical response functions obtainedin this way are power-law threshold singularities. Very recently it was realized that these singularities are in factmodified by the nonlinearities of the spectrum that are neglected in the LL approach. For cases where the ground state is made from a single species of fermions or bosons only, there exists a mapping of the thresholdsingularity problem to an effective X-ray edge problem for a mobile core hole. The latter is solvable and allows the determination ofsingularities in dynamical response functions. For applications such as Coulomb drag andmomentum resolved tunneling of electrons between quantum wires. For these applications it would be useful to knowthe structure of threshold singularities in the dynamical response of models of spinful electrons.Here one would expect a rich structure than in the single species case by virtue of the spin-charge separation at low energies.