Formal and Precise Derivation of the Green Functions for a Simple Potential

New derivation of Time-Independent Perturbation Theory

We propose a new derivation of Time-Independent Perturbation Theory (PT) that has a fundamental advantage over the usual derivations presented in textbooks on Quantum Mechanics (QM): it is simpler and much shorter. As such, it can provide an easier and quicker way for students to learn PT, than afforded by current methods. In spite of that, our approach does not require the potentials to be energy independent or the inverse free Green function $G_0^{-1}(E)$ to be a linear function of energy $E$, as is the case in QM, and can be applied directly to various extensions of QM including Relativisti…

Input-Output Formalism for Few-Photon Transport: A Systematic Treatment Beyond Two Photons

We provide a systematic treatment of $N$-photon transport in a waveguide coupled to a local system, using the input-output formalism. The main result of the paper is a general connection between the $N$-photon S matrix and the Green functions of the local system. We also show that the computation can be significantly simplified, by exploiting the connectedness structure of both the S matrix and the Green function, and by computing the Green function using an effective Hamiltonian that involves only the degrees of freedom of the local system. We illustrate our formalism by computing $N$-photon …

Electronic Transport in Electron-Phonon Gas of Two-Dimensional Holstein's Organic Molecular-Crystal: Non-equilibrium Green's Function Formalism & Boltzmann Transport Framework (A Generalized Mathematical Solution)

We have presented a consistent electronic transport framework for the two-dimensional extended Holstein's organic molecular-crystal based upon complete quantum-mechanical treatment through the non-equilibrium Green's function (NEGF) formalism and corresponding one-to-one semi-classical framework based upon Boltzmann transport theory for the narrow-bandwidth electronic energy organic semiconductor crystal material and device. In this process, we have formulated electronic self-energy interaction with acoustic and polar optical phonon mode with one phonon and two phonon interactions through Feyn…

基于第一性原理相互作用 Green 函数形式体系的激子–极化激元与激子局域化

Exciton-polaritons and exciton localization from a first-principles interacting Green's function formalism

提出基于 BSE 的从头算相互作用 Green 函数框架，以动力学电子–空穴交换作用描述激子–极化激元，并在多种材料中验证其局域化、偶极矩增强及色散预测能力。

球坐标系中自由狄拉克传播子的路径积分形式

Path integral formalism for the free Dirac propagator in spherical coordinates

本文在球坐标系中用费曼路径积分方法推导自由自旋1/2费米子的相对论格林函数，并通过坐标变换将其化为可精确求解的形式，结果用球贝塞尔函数和球旋量表示。

A Green's function formalism of energy and momentum transfer in fluctuational electrodynamics

Radiative energy and momentum transfer due to fluctuations of electromagnetic fields arising due to temperature difference between objects is described in terms of the cross-spectral densities of the electromagnetic fields. We derive relations between thermal non-equilibrium contributions to energy and momentum transfer and surface integrals of tangential components of the dyadic Green's functions of the vector Helmholtz equation. The expressions derived here are applicable to objects of arbitrary shapes, dielectric functions, as well as magnetic permeabilities. For the case of radiative trans…

A mathematical account of the NEGF formalism

The main goal of this paper is to put on solid mathematical grounds the so-called Non-Equilibrium Green's Function (NEGF) transport formalism for open systems. In particular, we derive the Jauho-Meir-Wingreen formula for the time-dependent current through an interacting sample coupled to non-interacting leads. Our proof is non-perturbative and uses neither complex-time Keldysh contours, nor Langreth rules of 'analytic continuation'. We also discuss other technical identities (Langreth, Keldysh) involving various many body Green's functions. Finally, we study the Dyson equation for the advanced…