Treatment of backscattering in a gas of interacting fermions confined to a one-dimensional harmonic atom trap

Journal Article · Sat Feb 01 04:00:00 EST 2003 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.67.023610· OSTI ID:20633751

Xianlong, Gao; Gleisberg, F; Lochmann, F; Wonneberger, W ^[1]

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1. Abteilung fuer Mathematische Physik, Universitaet Ulm, D89069 Ulm (Germany)

An asymptotically exact many-body theory for spin-polarized interacting fermions in a one-dimensional harmonic atom trap is developed using the bosonization method and including backward scattering. In contrast to the Luttinger model, backscattering in the trap generates one-particle potentials which must be diagonalized simultaneously with the two-body interactions. Inclusion of backscattering becomes necessary because backscattering is a dominant interaction process between confined identical one-dimensional fermions. The bosonization method is applied to the calculation of one-particle matrix elements at zero temperature. A detailed discussion of the validity of the results from bosonization is given, including a comparison with direct numerical diagonalization in fermionic Hilbert space. A model for the interaction coefficients is developed along the lines of the Luttinger model with only one coupling constant K. With these results, particle densities, the Wigner function, and the central pair-correlation function are calculated and displayed for large fermion numbers. It is shown how interactions modify these quantities. The anomalous dimension of the pair-correlation function in the center of the trap is also discussed and found to be in accord with the Luttinger model.

• OSTI ID: 20633751
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 2 Vol. 67; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
ANOMALOUS DIMENSION
ATOMS
BACKSCATTERING
BOSON EXPANSION
COMPARATIVE EVALUATIONS
CORRELATION FUNCTIONS
COUPLING CONSTANTS
DENSITY
FERMIONS
HILBERT SPACE
MATRIX ELEMENTS
ONE-DIMENSIONAL CALCULATIONS
POTENTIALS
RADIATION PRESSURE
SPIN
TRAPS
TWO-BODY PROBLEM