2003/06/30 by S. N. Artemenko, S N Artemenko, Gao Xianlong +2 · 12 citations
Mathematics · Physics and Astronomy · #Boundary (topology) #Boundary value problem #Cold Atom Physics and Bose-Einstein Condensates #Exponent #Friedel oscillations #Harmonic #Phase (matter) #Quantum many-body systems #Representation (politics) #Spectral Theory in Mathematical Physics #Trap (plumbing) #cond-mat.mes-hall #cond-mat.str-el #quant-ph
paper · pdf · doi:10.1088/0953-4075/37/7/052
published in Journal of Physics B Atomic Molecular and Optical Physics 37(7), S49-S58 (IOP Publishing) · Revised version to appear in Journal of Physics B: Atomic, Molecular and Optical Physics
arxiv created 2003/10/08 · openalex publication_date 2004/03/24 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Using an asymptotic phase representation of the particle density operator in the one-dimensional harmonic trap, the part which describes the Friedel oscillations is extracted. The expectation value 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.