论文标题
Tavis-Cummings和H $ \ BoldSymbol {\ ddot {u}} $ Ckel Hamiltonians具有对角线障碍的确切结果
Exact Results for the Tavis-Cummings and H$\boldsymbol{\ddot{u}}$ckel Hamiltonians with Diagonal Disorder
论文作者
论文摘要
我们提出了一种确切的方法来计算一个具有对角线障碍的电子哈密顿电子的电子状态。我们表明，可以使用确定性的复合物（非热）汉密尔顿人直接计算出一种粒子绿色功能的疾病。为此，我们假设分子状态具有Cauchy（Lorentz）分布，并使用已经用于固态物理问题的超对称方法。使用该方法，我们以任何$ n $的值找到了$ n $分子的确切解决方案，仅限于微腔。我们的分析表明，极化状态的宽度随$ n $的函数取决于疾病的性质，因此可以用来探测分子能级分布的方式。我们还展示了如何找到H $ \ ddot {U} $ CKEL型汉密尔顿人患有现场，库奇疾病的确切结果并证明其使用。
We present an exact method to calculate the electronic states of one electron Hamiltonians with diagonal disorder. We show that the disorder averaged one particle Green's function can be calculated directly, using a deterministic complex (non-Hermitian) Hamiltonian. For this, we assume that the molecular states have a Cauchy (Lorentz) distribution and use the supersymmetric method which has already been used in problems of solid state physics. Using the method we find exact solutions to the states of $N$ molecules, confined to a microcavity, for any value of $N$. Our analysis shows that the width of the polaritonic states as a function of $N$ depend on the nature of disorder, and hence can be used to probe the way molecular energy levels are distributed. We also show how one can find exact results for H$\ddot{u}$ckel type Hamiltonians with on-site, Cauchy disorder and demonstrate its use.
