### Abstract

Using an asymptotic phase representation of the particle density operator ρ̂(z) in the one-dimensional harmonic trap, the part δ ρ̂_{F}(z) which describes the Friedel oscillations is extracted. The expectation value 〈δ ρ̂_{F}(z)〉 with respect to the interacting ground state requires the calculation of the mean square average of a properly defined phase operator. This calculation is performed analytically for the Tomonaga-Luttinger model with harmonic confinement. It is found that the envelope of the Friedel oscillations at zero temperature decays with the boundary exponent ν = (K + 1)/2 away from the classical boundaries. This value differs from that known for open boundary conditions or strong pinning impurities. The soft boundary in the present case thus modifies the decay of Friedel oscillations. The case of two components is also discussed.

Original language | English |
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Journal | Journal of Physics B: Atomic, Molecular and Optical Physics |

Volume | 37 |

Issue number | 7 |

DOIs | |

Publication status | Published - 14 Apr 2004 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics
- Condensed Matter Physics

### Cite this

**Friedel oscillations in a gas of interacting one-dimensional fermionic atoms confined in a harmonic trap.** / Artemenko, S. N.; Xianlong, Gao; Wonneberger, W.

Research output: Contribution to journal › Article

*Journal of Physics B: Atomic, Molecular and Optical Physics*, vol. 37, no. 7. https://doi.org/10.1088/0953-4075/37/7/052

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TY - JOUR

T1 - Friedel oscillations in a gas of interacting one-dimensional fermionic atoms confined in a harmonic trap

AU - Artemenko, S. N.

AU - Xianlong, Gao

AU - Wonneberger, W.

PY - 2004/4/14

Y1 - 2004/4/14

N2 - Using an asymptotic phase representation of the particle density operator ρ̂(z) in the one-dimensional harmonic trap, the part δ ρ̂F(z) which describes the Friedel oscillations is extracted. The expectation value 〈δ ρ̂F(z)〉 with respect to the interacting ground state requires the calculation of the mean square average of a properly defined phase operator. This calculation is performed analytically for the Tomonaga-Luttinger model with harmonic confinement. It is found that the envelope of the Friedel oscillations at zero temperature decays with the boundary exponent ν = (K + 1)/2 away from the classical boundaries. This value differs from that known for open boundary conditions or strong pinning impurities. The soft boundary in the present case thus modifies the decay of Friedel oscillations. The case of two components is also discussed.

AB - Using an asymptotic phase representation of the particle density operator ρ̂(z) in the one-dimensional harmonic trap, the part δ ρ̂F(z) which describes the Friedel oscillations is extracted. The expectation value 〈δ ρ̂F(z)〉 with respect to the interacting ground state requires the calculation of the mean square average of a properly defined phase operator. This calculation is performed analytically for the Tomonaga-Luttinger model with harmonic confinement. It is found that the envelope of the Friedel oscillations at zero temperature decays with the boundary exponent ν = (K + 1)/2 away from the classical boundaries. This value differs from that known for open boundary conditions or strong pinning impurities. The soft boundary in the present case thus modifies the decay of Friedel oscillations. The case of two components is also discussed.

UR - http://www.scopus.com/inward/record.url?scp=2342477993&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=2342477993&partnerID=8YFLogxK

U2 - 10.1088/0953-4075/37/7/052

DO - 10.1088/0953-4075/37/7/052

M3 - Article

AN - SCOPUS:2342477993

VL - 37

JO - Journal of Physics B: Atomic, Molecular and Optical Physics

JF - Journal of Physics B: Atomic, Molecular and Optical Physics

SN - 0953-4075

IS - 7

ER -