JIT (UEG) dielectric

A forked/imported version of ueg-dielectric - numerical methods to compute the finite-temperature random phase approximation and Mermin dielectric functions of a uniform electron gas (UEG) with JIT compilation.

Introduction

The dielectric function is a wave vector and frequency dependent generalization of the macroscopic dielectric constant $\epsilon$ used in theory of linear dielectric media that relates the electric displacement field $\mathbf{D}$ and the electric field $\mathbf{E}$: $\mathbf{D} = \epsilon \mathbf{E}$. It ultimately describes how the electrons in a material respond to some external electromagnetic perturbation or force. The dielectric function is important because it is related to many observable quantities in the linear response regime, like the dynamic structure factor (which is measured in scattering experiments) and the stopping power (which is important in inertial confinement fusion experiments).

This module computes the complex, quantum mechanical dielectric function for a uniform electron gas using two popular approaches:

1. The random phase approximation (e.g. Johnson, Nilsen, and Cheng, 2012) and
2. The Mermin ansatz (Mermin, 1970), which modifies the electron gas dielectric function to more accurately represent electrons in the real material by incorporating an electron-ion collision rate.

Getting Started

Note: all quantities are in atomic units¹

We use ElectronGas class objects to hold the physical information about the electrons (e.g. temperature/thermal energy, electron density)

from uegdielectric import ElectronGas

# thermal energy of electrons
t = 3.17E-2 # atomic units - approximately 10,000 kelvin
# electron density
d = 2.68e-02 # atomic units - approximately 1.53e16 electrons per centimeters cubed
electrons = ElectronGas(t, d)

We can use either the RPA or Mermin classes to compute the complex dielectric function as a function of wave number wavenum and frequency frequency. For the Mermin model, we can also provide an electron-ion collision rate collisionrate, which is assumed to be frequency dependent.

from uegdielectric import dielectric
eps = dielectric.RPA(electrons)
# wave number
q = 1.0 # atomic units
# frequency
omega = 0.5 # atomic units
# dielectric object is callable!
eps(wavenum=q, frequency=omega)
>>> (1.452804827343392+0.8463619935408268j)

More examples are being added to the docs/notebooks directory.

Requirements

UEG dielectric supports Python ≥ 3.11.

Installation

Install the latest GitHub main version using pip:

pip install git+https://github.com/twhentschel/jit-dielectric.git

Footnotes

1. See this Wikipedia article for an introduction to atomic units. ↩