Spectral estimates in the presence of a magnetic field

对积分算子特征值的估计是量子现象和相关数学领域研究中许多结果的核心。本项目旨在建立包含磁场的量子模型中产生的积分算符的详细光谱性质。预期的目标是在分析中产生新的和重要的理论结果，这将打开使用磁微分算子的新方法。预计这将通过加强数学和理论物理之间的合作，通过提供与新兴量子科学技术相关的研究培训，以及加强与世界领先科学家的研究合作，使澳大利亚科学受益。

Estimates on eigenvalues of integral operators are at the core of numerous results in the study of quantum phenomena and in associated mathematical fields. This project aims to establish detailed spectral properties of the integral operators arising in quantum models incorporating magnetic fields. An anticipated goal is the generation of new and significant theoretical results in analysis that will open novel approaches to the use of magnetic differential operators. This is expected to benefit Australian science by invigorating collaboration between mathematics and theoretical physics, by providing research training relevant to emerging quantum science based technology and strengthening research collaborations with world leading scientists.