应6163银河net163am和萃英学院邀请，德国达姆施塔特工业大学Barbara Dietz研究员来我校访问，并于10月28日、10月30日、11月2日分别作学术报告，敬请大家关注。
报告题目：Experiments with Superconducting Microwave Resonators Emulating Artificial Graphene and Fullerene C60
报告摘要：We determined experimentally the eigenvalues of quantum billiards with the shapes of a rectangle and of Africa, respectively, that contain circular scatterers forming a triangular grid, so-called Dirac billiards. For this, high-precision measurements have been performed with superconducting microwave billiards. We investigated the particular features of the density of the eigenvalues (DOE), which resembles that of a graphene flake, and of their fluctuation properties. I will demonstrate in my talk that the van Hove singularities, that show up as sharp peaks in the DOE, divide the associated band into regions where the system is governed by the non-relativistic Schr?dinger equation of the quantum billiard and the Dirac equation of the graphene billiard of corresponding shape, respectively. Furthermore, experiments have been performed using a spherical superconducting microwave resonator with the geometric structure of the C$_{60}$ fullerene molecule in order to, firstly, study with very high resolution the exceptional spectral properties emerging from the symmetries of the icosahedral structure of the carbon lattice. Secondly, we determined the number of zero modes with eigenvalues at the Dirac point to test the predictions of the Atiyah-Singer index theorem, which relates it to the topology of the curved carbon lattice.
报告题目：Spectral Properties and Dynamical Tunneling in Constant-Width Billiards
报告摘要：We determined with unprecedented accuracy the lowest 900 eigenvalues of two quantum billiards with the shapes of constant-width billiards from resonance spectra measured with superconducting microwave billiards. While the classical dynamics of the constant-width billiards is unidirectional, a change of the direction of motion is possible in the corresponding quantum billiard via dynamical tunneling. This becomes manifest in a splitting of the vast majority of resonances into doublets of nearly degenerate ones. The fluctuation properties of the two respective spectra are demonstrated to coincide with those of a random-matrix model applicable to systems with violated time-reversal invariance and a mixed dynamics. Furthermore, we investigated tunneling in terms of the splittings of the doublet partners. On the basis of a random-matrix model we derived an analytical expression for the splitting distribution which is generally applicable to systems exhibiting dynamical tunneling between two regions with (predominantly) chaotic dynamics.
报告题目：Chaotic scattering in the region of overlapping resonances in systems with induced
violation of time-reversal invariance
报告摘要：We measured the transmission and reflection spectra of a chaotic microwave billiard in the regions of isolated and overlapping resonances. By placing a magnetized ferrite inside the cavity, breaking of time-reversal (T) invariance was induced. The T-breaking effect of the ferrite varies with the excitation frequency. Only partial T-breaking is achievable. For the random-matrix theoretical description of fluctuation properties of the measured scattering matrix elements, a scattering approach originally developed in the context of compound nucleus reactions is used. Based on this scattering formalism and the supersymmetry method, we derived analytic expressions for the autocorrelation and the cross-correlation functions of pairs of complex conjugate scattering matrix elements. This model is applicable in the regions of isolated and of overlapping resonances and depends on a parameter, which defines the strength of the T-breaking. By fitting it to the scattering data we determined the strength of T-violation for the whole range of the excitation frequency. Furthermore, the elastic enhancement factor was determined as function of the excitation frequency. A comparison with theoretical predictions provides another confirmation of the model.
Dietz研究员主要从事复杂量子系统的研究，包括量子混沌、随机矩阵理论、超导微波谐振腔等相关领域的理论和实验研究。借助二维超导微波谐振腔实验，用微波及光子晶格来模拟复杂量子系统，在经典不可积系统对应的量子系统的能谱及波函数特征、用光子晶格来模拟人工石墨烯、用非线性微波介质来模拟量子多体系统等方面的出色工作，对理解经典量子对应中的一些基本物理问题做出了重要贡献。在这些领域中发表论文 60 余篇，其中Phys. Rev. Lett. 12 篇，部分成果写入Haake博士的‘Quantum Signatures of Chaos’ 以及Mehta博士的‘Random Matrices’ 两本著作当中。作过三十余次国际会议和德国国内报告，组织过两次国际会议。研究工作自2002年起受German Research Foundation (DFG) 资助，在微波及光子晶格实验模拟复杂量子系统方面的工作，对经典量子对应中的一些基本物理问题的理解起了重要的推动作用。
