论文标题
BCS理论在弱磁场状态下用于非零通量和在扩展量子晶格系统中绝热定理的指数估计的系统
BCS Theory in the Weak Magnetic Field Regime for Systems with Nonzero Flux and Exponential Estimates on the Adiabatic Theorem in Extended Quantum Lattice Systems
论文作者
论文摘要
在本博士学位论文的主要部分中，我们考虑了由BCS理论描述的定期实现的显微镜超导体，该超导体受外部电磁场的影响。我们表明，在宏观和弱磁场限制中，金兹堡 - 兰道理论正确地描述了超导体。我们结果的主要新颖性是允许通过周期性晶格的单位电池进行非变化的磁通量。这些主要结果是由BCS理论领域的各种未发表的注释补充。此外，我们以适合硕士或博士学位的学生的全面介绍来介绍这些结果。因此，我们希望为填补该领域缺少入门文献的空白做出贡献。 该论文包括第二个主题，其中我们为建立量子晶格系统提供了想法，以证明对绝热定理的指数估计。这些笔记是该领域研究的结果，该研究是在加拿大温哥华不列颠哥伦比亚大学（UBC）的研究期间进行的。
In the main part of this PhD thesis, we consider a periodically realized microscopic superconductor described by BCS theory, which is subject to external electromagnetic fields. We show that the superconductor is properly described by Ginzburg--Landau theory in the macroscopic and weak magnetic field limit. The main novelty of our results is to allow for a non-vanishing magnetic flux through the unit cell of the lattice of periodicity. These main results are supplemented by various unpublished notes in the field of BCS theory. Furthermore, we preface the presentation of these results with a comprehensive introduction suitable for master's or PhD students. Thereby, we hope to contribute to filling the gap of missing introductory literature in the field. The thesis comprises a second topic, in which we provide ideas for setting up quantum lattice systems in order to prove exponential estimates for the adiabatic theorem. These notes are the result of studies in this field, which have been conducted during a research stay at the University of British Columbia (UBC) in Vancouver, Canada.
