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Title: Exact numerical simulations of a one-dimensional trapped Bose gas

Abstract

We analyze the ground-state and low-temperature properties of a one-dimensional Bose gas in a harmonic trapping potential using the numerical density-matrix renormalization group. Calculations cover the whole range from the Bogoliubov limit of weak interactions to the Tonks-Girardeau limit. Local quantities such as density and local three-body correlations are calculated and shown to agree very well with analytic predictions within a local-density approximation. The transition between temperature-dominated to quantum-dominated correlation is determined. It is shown that despite the presence of the harmonic trapping potential, first-order correlations display, over a large range, the algebraic decay of a harmonic fluid with a Luttinger parameter determined by the density at the trap center.

Authors:
;  [1]
  1. Fachbereich Physik, Technische Universitaet, Kaiserslautern, D-67663 Kaiserslautern (Germany)
Publication Date:
OSTI Identifier:
20982055
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevA.75.021601; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; BOSE-EINSTEIN GAS; BOSONS; CORRELATIONS; DENSITY FUNCTIONAL METHOD; DENSITY MATRIX; FORECASTING; GROUND STATES; NUMERICAL ANALYSIS; ONE-DIMENSIONAL CALCULATIONS; POTENTIALS; RENORMALIZATION; SIMULATION; TEMPERATURE RANGE 0065-0273 K; THREE-BODY PROBLEM; TRAPPING; TRAPS; WEAK INTERACTIONS

Citation Formats

Schmidt, Bernd, and Fleischhauer, Michael. Exact numerical simulations of a one-dimensional trapped Bose gas. United States: N. p., 2007. Web. doi:10.1103/PHYSREVA.75.021601.
Schmidt, Bernd, & Fleischhauer, Michael. Exact numerical simulations of a one-dimensional trapped Bose gas. United States. doi:10.1103/PHYSREVA.75.021601.
Schmidt, Bernd, and Fleischhauer, Michael. Thu . "Exact numerical simulations of a one-dimensional trapped Bose gas". United States. doi:10.1103/PHYSREVA.75.021601.
@article{osti_20982055,
title = {Exact numerical simulations of a one-dimensional trapped Bose gas},
author = {Schmidt, Bernd and Fleischhauer, Michael},
abstractNote = {We analyze the ground-state and low-temperature properties of a one-dimensional Bose gas in a harmonic trapping potential using the numerical density-matrix renormalization group. Calculations cover the whole range from the Bogoliubov limit of weak interactions to the Tonks-Girardeau limit. Local quantities such as density and local three-body correlations are calculated and shown to agree very well with analytic predictions within a local-density approximation. The transition between temperature-dominated to quantum-dominated correlation is determined. It is shown that despite the presence of the harmonic trapping potential, first-order correlations display, over a large range, the algebraic decay of a harmonic fluid with a Luttinger parameter determined by the density at the trap center.},
doi = {10.1103/PHYSREVA.75.021601},
journal = {Physical Review. A},
number = 2,
volume = 75,
place = {United States},
year = {Thu Feb 15 00:00:00 EST 2007},
month = {Thu Feb 15 00:00:00 EST 2007}
}
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  • No abstract prepared.
  • We consider two regimes where a trapped Bose gas behaves as a one-dimensional (1D) system. In the first one the Bose gas is microscopically described by 3D mean-field theory, but the trap is so elongated that it behaves as a 1D gas with respect to low-frequency collective modes. In the second regime we assume that the 1D gas is truly 1D and that it is properly described by the Lieb-Liniger model. In both regimes we find the frequency of the lowest compressional mode by solving the hydrodynamic equations. This is done by making use of a method which allows usmore » to find analytical or quasianalytical solutions of these equations for a large class of models approaching very closely the actual equation of state of the Bose gas. We find an excellent agreement with the recent results of Menotti and Stringari obtained from a sum-rule approach.« less