Version 1
: Received: 21 February 2024 / Approved: 22 February 2024 / Online: 22 February 2024 (09:52:46 CET)
How to cite:
Stephenson, M.J. Non-Linear Coordinate Transformations at Homogeneous Electron Gases. Preprints2024, 2024021290. https://doi.org/10.20944/preprints202402.1290.v1
Stephenson, M.J. Non-Linear Coordinate Transformations at Homogeneous Electron Gases. Preprints 2024, 2024021290. https://doi.org/10.20944/preprints202402.1290.v1
Stephenson, M.J. Non-Linear Coordinate Transformations at Homogeneous Electron Gases. Preprints2024, 2024021290. https://doi.org/10.20944/preprints202402.1290.v1
APA Style
Stephenson, M.J. (2024). Non-Linear Coordinate Transformations at Homogeneous Electron Gases. Preprints. https://doi.org/10.20944/preprints202402.1290.v1
Chicago/Turabian Style
Stephenson, M.J. 2024 "Non-Linear Coordinate Transformations at Homogeneous Electron Gases" Preprints. https://doi.org/10.20944/preprints202402.1290.v1
Abstract
We explores the hydrodynamical limit of a homogeneous electron gas, considering the interplay between the infrared limit and phenomenological hydrodynamics. Our study involves interactions generated by non-linear coordinate transformations. The focus begins with an analysis of non-linear coordinate transformations and their impact on normal modes in a harmonic system. The Lagrangian for a harmonic oscillator is used as an illustrative example, highlighting the role of position-dependent effective mass in preventing certain coordinate values. Moving beyond single degrees of freedom, we extend the discussion to a system with several harmonic degrees of freedom, introducing a collective variable. The effective dynamics of this collective variable are defined through a Lagrange multiplier term, emphasizing linearity in the description. Our study extends to the Current Two-Point function (CTP) formalism, introducing matrices and their inverses, such as $\hD$ and $\hD^{-1}$. Further, we delve into the dynamics of current in a homogeneous electron gas at finite density and zero temperature. Green's functions are generated using a functional integral approach, and the effective action is constructed via functional Legendre transformation. The quadratic part of the generator functional is expanded to derive the effective action, leading to the Maxwell equation and the subsequent elimination of the photon field. The resulting effective action for current dynamics is expressed in terms of the Current Two-Point function, paving the way for further exploration of the hydrodynamical aspects of the electron gas. Our study combines theoretical developments and mathematical formalism to provide insights into the hydrodynamical behavior of homogeneous electron gases.
Keywords
Hydrodynamical limit; Homogeneous electron gases; Non-linear coordinate transformations; Infrared limit; Phenomenological hydrodynamics; Normal modes; Harmonic system
Subject
Physical Sciences, Mathematical Physics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
