The Dirac-Frenkel Principle for Reduced Density Matrices, and the Bogoliubov-de-Gennes Equations

Bogoliubov-de Gennes方程中的配对

Pairing in the Bogoliubov-de Gennes equations

结果表明，Bogoliubov-de Gennes方程对电子的状态是正常状态的线性组合。因此，需要BCS样归约过程来选择正确的配对。对于齐次系统，我们指出由Bogoliubov-de Gennes方程导出的自洽方程的核需要受到BCS配对条件的约束。另一方面，在存在普通杂质的情况下，Bogoliubov-de Gennes方程应补充Anderson的配对条件，以通过相应的幺正变换获得正确的真空态。这导致声子介导的相互作用的局部化校正。

Vortex Lattices and the Bogoliubov-De Gennes Equations

We consider the Bogoliubov-de Gennes equations giving an equivalent formulation of the BCS theory of superconductivity. We are interested in static solutions with the magnetic field present. We carefully formulate the equations in the basis independent form, discuss their general features and isolate key physical classes of solutions (normal and vortex lattice states) which are the candidates for the ground state. We prove existence of the normal and vortex lattice states and stability of the normal states for large temperature or magnetic fields and their instability for small temperature and…

Bogoliubov-de Gennes方程的电子-空穴相干态

Electron-hole coherent states for the Bogoliubov-de Gennes equation

我们构造了无限直线上（准）自旋粒子的一组新的广义相干态--电子-空穴相干态。这个定义的灵感来自于Bogoliubov-de Gennes方程的应用，其中准自旋是指超导体中电子激发的电子和空穴成分。电子-空穴相干态一般纠缠空间和准自旋自由度。我们表明，电子-空穴相干态允许获得一个统一的决议，并形成最小的不确定性状态的位置和速度的速度算子定义使用Bogoliubov-德Gennes哈密顿。讨论了电子-空穴相干态的有用性和局限性以及由它们建立的相空间表示在Bogoliubov-de Gennes方程的基本应用方面，如Andreev反射。

Bogoliubov/de Gennes系统、AKNS体系和非线性量子力学超对称性

The Bogoliubov/de Gennes system, the AKNS hierarchy, and nonlinear quantum mechanical supersymmetry

我们表明，Ginzburg-Landau展开的大潜力的Bogoliubov-德Gennes哈密顿量是由可积的非线性方程的AKNS系列，这提供了一个隐藏的非线性量子力学超对称性的动力学的自然数学框架。

The one dimensional semi-classical Bogoliubov-de Gennes Hamiltonian with PT symmetry: generalized Bohr-Sommerfeld quantization rules

We present a method for computing first order asymptotics of semiclassical spectra for 1-D Bogoliubov-de Gennes (BdG) Hamiltonian from Supraconductivity, which models the electron/hole scattering through two SNS junctions. This involves: 1) reducing the system to Weber equation near the branching point at the junctions, 2) constructing local sections of the fibre bundle of microlocal solutions, 3) normalizing these solutions for the "flux norm" associated to the microlocal Wronskians, 4) finding the relative monodromy matrices in the gauge group that leaves invariant the flux norm, 5) from thi…

Andreev反射和半经典Bogoliubov-de Gennes哈密顿量：共振态

Andreev reflection and the semiclassical Bogoliubov-de Gennes Hamiltonian: resonant states

我们提出了一个半经典的分析门控介观SNS结的超通道的开放。对于完美的结（即硬壁势），这是由Chtchelkatchev，Lesovik和Blatter在散射矩阵的框架中考虑的。在这里，我们允许在结的缺陷，使复杂的序参量继续作为一个光滑的函数，这是一个常数的超导银行，并迅速消失内的铅。我们得到了费米能级附近的共振Andreev态的量子化规则，包括共振宽度的确定。