2003/01/14 by Diptiman Sen · 1 citation
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Quantum, superfluid, helium dynamics #Strong Light-Matter Interactions #cond-mat.str-el
paper · pdf · doi:10.1088/0305-4470/36/27/305
published as J. Phys. A 36 (2003) 7517 · LaTeX, 17 pages, no figures
arxiv created 2003/01/14 · openalex publication_date 2003/06/24 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
We use first-order perturbation theory near the fermionic limit of the δ-function Bose gas in one dimension (i.e. a system of weakly interacting fermions) to study three situations of physical interest. The calculation is done using a pseudopotential which takes the form of a two-body δ''-function interaction. The three cases considered are the behaviour of the system with a hard wall, with a point where the strength of the pseudopotential changes discontinuously, and with a region of finite length where the pseudopotential strength is non-zero (this is sometimes used as a model for a quantum wire). In all cases, we obtain exact expressions for the density to first order in the pseudopotential strength. The asymptotic behaviour of the densities is in agreement with the results obtained from bosonization for a Tomonaga–Luttinger liquid, namely, an interaction dependent power-law decay of the density far from the hard wall, a reflection from the point of discontinuity and transmission resonances for the interacting region of finite length. Our results provide a non-trivial verification of the Tomonaga–Luttinger liquid description of the δ-function Bose gas near the fermionic limit.