Transformation of the Eilenberger Equations of Superconductivity to a Scalar Riccati Equation
Transformation of the Eilenberger Equations of Superconductivity to a Scalar Riccati Equation
复制标题
超导 Eilenberger 方程到标量 Riccati 方程的变换
DOI：
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
N. Schopohl
中科院分区：
文献类型：
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作者：
N. Schopohl
本文介绍了用Riccati型标量微分方程的解来参数化超导Eilenberger方程的一种新方法。它示出的准经典传播，特别是局域态密度，可以重建，没有明确的知识的任何本征函数和本征值，通过解决一个简单的初始值问题的线性化Bogoliubov-德Gennes方程。准经典传播子的Riccati参数化导致了求解Eilenberger方程的稳定且快速的数值方法。对于某些空间变化的模型对势的Eilenberger方程的精确解的发现。
A new parametrisation of the Eilenberger equations of superconductivity in terms of the solutions to a scalar differential equation of the Riccati type is introduced. It is shown that the quasiclassical propagator, and in particular the local density of states, may be reconstructed, without explicit knowledge of any eigenfunctions and eigenvalues, by solving a simple initial value problem for the linearised Bogoliubov-de Gennes equations. The Riccati parametrisation of the quasiclassical propagator leads to a stable and fast numerical method to solve the Eilenberger equations. For some spatially varying model pair potentials exact solutions to the Eilenberger Equations are found.