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1d results for l=3 have been obtained in Ref. within a hydrodynamical model, whereas for l=2, ωBM is known to be λ independent (Ref.).
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1d results for l=3 have been obtained in Ref. within a hydrodynamical model, whereas for l=2, ωBM is known to be λ independent (Ref.).
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We should note, that both excitations, (I) and (II), have vanishing dipole moments. Therefore, no dipole oscillation, as, e.g., the well-known Kohn mode, can be excited.
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We should note, that both excitations, (I) and (II), have vanishing dipole moments. Therefore, no dipole oscillation, as, e.g., the well-known Kohn mode, can be excited.
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Note that for other types of excitation other center-of-mass motions will be observed. In particular, a dipole excitation will give rise to the familiar sloshing or Kohn mode which is independent of N, dimensionality, interaction or quantum, and spin effects.
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Note that for other types of excitation other center-of-mass motions will be observed. In particular, a dipole excitation will give rise to the familiar sloshing or Kohn mode which is independent of N, dimensionality, interaction or quantum, and spin effects.
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E-PRBMDO-80-055929 for a video illustrating the oscillation behavior of two particles in 2D. For more information on EPAPS, see
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See EPAPS Document No. E-PRBMDO-80-055929 for a video illustrating the oscillation behavior of two particles in 2D. For more information on EPAPS, see http://www.aip.org/pubservs/epaps.html.
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20
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70249114738
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For 1/ r2 interaction the existence of a twofold degenerate BM with ωR = ωr =2 was reported in Ref..
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For 1/ r2 interaction the existence of a twofold degenerate BM with ωR = ωr =2 was reported in Ref..
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In contrast, φ0A vanishes at the singularity and the numerical result for ωr is correct, in the limit of small κ. Hence, we used φ0A in our 1D calculations.
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In contrast, φ0A vanishes at the singularity and the numerical result for ωr is correct, in the limit of small κ. Hence, we used φ0A in our 1D calculations.
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24
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70249116012
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In 2D, the Coulomb integrals converge and no cut-off parameter κ is required.
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In 2D, the Coulomb integrals converge and no cut-off parameter κ is required.
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70249137548
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The limits, ωr (0) = 2.0 and ωr (λ→∝) =3 are built in. In 1D (2D) the parameters are b=0.867 (b=0.204) and c=1.742 (c=0.296).
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The limits, ωr (0) =2.0 and ωr (λ→∝) =3 are built in. In 1D (2D) the parameters are b=0.867 (b=0.204) and c=1.742 (c=0.296).
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