Dispersion relation and spectral function of an impurity in a one-dimensional quantum liquid

Abstract

We consider the motion of an impurity particle in a general one-dimensional quantum fluid at zero temperature. The dispersion relation $\Omega (P)$ of the impurity is strongly affected by interactions with the fluid as the momentum approaches $\pm \pi \hslash n,\pm 3\pi \hslash n,...$, where $n$ is the density. This behavior is caused by singular $\pm 2\pi \hslash n$ scattering processes and can be understood by analogy to the Kondo effect, both at strong and weak coupling, with the possibility of a quantum phase transition where ${\Omega }^{\prime }(\pm \pi n)$ jumps to zero with increasing coupling. The low energy singularities in the impurity spectral function can be understood on the same footing.

Published version

References in corpus (4)

• Many-Body Physics with Ultracold Gases
• Quantum transport through a Tonks-Girardeau gas
• Spin dynamics in a one-dimensional ferromagnetic Bose gas
• Spectral functions of strongly interacting isospin-1/2 bosons in one dimension

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