English

Fermionic Phonons: Exact Analytic Results and Quantum Statistical Mechanics for a One Dimensional Harmonic Crystal

Quantum Physics 2021-08-30 v3 Statistical Mechanics Chemical Physics

Abstract

Analytic expressions for the energy eigenvalues and eigenfunctions of a one-dimensional harmonic crystal are obtained. The average energy and density profiles are obtained numerically as a function of temperature. A surprisingly large number of energy levels (eg.\ 5,000 for 4 particles) are required for reliable results at even moderate temperatures.

Keywords

Cite

@article{arxiv.1903.06866,
  title  = {Fermionic Phonons: Exact Analytic Results and Quantum Statistical Mechanics for a One Dimensional Harmonic Crystal},
  author = {Phil Attard},
  journal= {arXiv preprint arXiv:1903.06866},
  year   = {2021}
}

Comments

9 pages, 5 sections, 5 figures. Total = 19. Erroneous wave function symmetrization results now removed

R2 v1 2026-06-23T08:10:04.108Z