dorsal/arxiv
View SchemaNon-Interacting Fermions in a One-Dimensional Harmonic Atom Trap: Exact One-Particle Properties at Zero Temperature
| Authors | F. Gleisberg, W. Wonneberger, U. Schloeder, C. Zimmermann |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0009085 |
| URL | https://arxiv.org/abs/quant-ph/0009085 |
| DOI | 10.1103/PhysRevA.62.063602 |
| Journal | Phys.Rev. A, 63602 (2000) |
Abstract
One-particle properties of non-interacting Fermions in a one-dimensional harmonic trap and at zero temperature are studied. Exact expressions and asymptotic results for large Fermion number N are given for the particle density distribution n_0(z,N). For large N and near the classical boundary at the Fermi energy the density displays increasing fluctuations. A simple scaling of these tails of the density distribution with respect to N is established. The Fourier transform of the density distribution is calculated exactly. It displays a small but characteristic hump near 2 k_F with k_F being a properly defined Fermi wave number. This is due to Friedel oscillations which are identified and discussed. These quantum effects are missing in the semi-classical approximation. Momentum distributions are also evaluated and discussed. As an example of a time-dependent one-particle problem we calculate exactly the evolution of the particle density when the trap is suddenly switched off and find a simple scaling behaviour in agreement with recent general results.
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"abstract": "One-particle properties of non-interacting Fermions in a one-dimensional\nharmonic trap and at zero temperature are studied. Exact expressions and\nasymptotic results for large Fermion number N are given for the particle\ndensity distribution n_0(z,N). For large N and near the classical boundary at\nthe Fermi energy the density displays increasing fluctuations. A simple scaling\nof these tails of the density distribution with respect to N is established.\nThe Fourier transform of the density distribution is calculated exactly. It\ndisplays a small but characteristic hump near 2 k_F with k_F being a properly\ndefined Fermi wave number. This is due to Friedel oscillations which are\nidentified and discussed. These quantum effects are missing in the\nsemi-classical approximation. Momentum distributions are also evaluated and\ndiscussed. As an example of a time-dependent one-particle problem we calculate\nexactly the evolution of the particle density when the trap is suddenly\nswitched off and find a simple scaling behaviour in agreement with recent\ngeneral results.",
"arxiv_id": "quant-ph/0009085",
"authors": [
"F. Gleisberg",
"W. Wonneberger",
"U. Schloeder",
"C. Zimmermann"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.62.063602",
"journal_ref": "Phys.Rev. A, 63602 (2000)",
"title": "Non-Interacting Fermions in a One-Dimensional Harmonic Atom Trap: Exact One-Particle Properties at Zero Temperature",
"url": "https://arxiv.org/abs/quant-ph/0009085"
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