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-dimensional interacting fermions in the harmonic trap is investigated and a suitable modification of the interaction is proposed which preserves the Kohn mode. The modified theory is used to calculate exactly the inhomogeneous linear mobility mu(z, z(0); w) at position z in response to a spatial force pulse at position z(0). It is found that the inhomogeneous particle mobility exhibits resonances not only at the trap frequency we but also at multiples m (epsilon) over tilde, m = 2, 3,... of a new renormalized collective mode frequency which depends on the strength of the interaction. In contrast, the homogeneous response obtained by an average over z(0) remains that of the non-interacting system. (c) 2006 Elsevier B.V. All rights reserved.