Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2003-06-24
Physics
Condensed Matter
Strongly Correlated Electrons
Revised version to appear in Journal of Physics B: Atomic, Molecular and Optical Physics
Scientific paper
10.1088/0953-4075/37/7/052
Using an asymptotic phase representation of the particle density operator $\hat{\rho}(z)$ in the one-dimensional harmonic trap, the part $\delta \hat{\rho}_F(z)$ which describes the Friedel oscillations is extracted. The expectation value $<\delta \hat{\rho}_F(z)>$ 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 $\nu = (K+1)/2$ 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.
Artemenko S. N.
Wonneberger W.
Xianlong Gao
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