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Abstract: We study equilibrium density and spin density profiles for a model of coldone-dimensional spin 1-2 fermions interacting via inverse square interactionand exchange in an external harmonic trap. This model is the well-knownspin-Calogero model sCM and its fully nonlinear collective field theorydescription is known. We extend the field theory description to the presence ofan external harmonic trap and obtain analytic results for statics and dynamicsof the system. For instance, we find how the equilibrium density profilechanges upon tuning the interaction strength. The results we obtain forequilibrium configurations are very similar to the ones obtained recently by Maand Yang 1 for a model of fermions with short ranged interactions. Our mainapproximation is the neglect of the terms of higher order in spatialderivatives in equations of motion - gradientless approximation 2. Withinthis approximation the hydrodynamic equations of motion can be written as a setof decoupled forced Riemann-Hopf equations for the dressed Fermi momenta of themodel. This enables us to write analytical solutions for the dynamics of spinand charge. We describe the time evolution of the charge density when aninitial non-equilibrium profile is created by cooling the gas with anadditional potential in place and then suddenly removing the potential. Wepresent our results as a simple -single-particle- evolution in the phase-spacereminiscing a similar description of the dynamics of non-interactingone-dimensional fermions.



Author: M. Kulkarni, A. G. Abanov

Source: https://arxiv.org/







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