Dynamic response of interacting one-dimensional fermions in the harmonic atom trap: Phase response and the inhomogeneous mobility

摘要

The problem of the Kohn mode in bosonized theories of one-dimensionalinteracting fermions in the harmonic trap is investigated and a suitablemodification of the interaction is proposed which preserves the Kohn mode. Themodified theory is used to calculate exactly the inhomogeneous linear mobilityat position z in response to a spatial force pulse at another position. It isfound the inhomogeneous particle mobility exhibits resonances not only at thetrap frequency but also at multiples of a new renormalized collective modefrequency which depends on the strength of the interaction. In contrast, thelocal response obtained by averaging over the pulse position remains that ofthe non-interacting system.