Dynamics of a heavy particle in a Luttinger liquid

Abstract

We study the dynamics of a heavy particle of mass $M$ moving in a one-dimensional repulsively interacting Fermi gas. The Fermi gas is described using the Luttinger model and bosonization. By transforming to a frame co-moving with the heavy particle, we map the model onto a generalized ``quantum impurity problem". A renormalization group calculation reveals a crossover from strong to weak coupling upon scaling down in temperature. Above the crossover temperature scale $T^{\ast }=(m/M)E_F$, the particle's mobility, $\mu$, is found to be (roughly) temperature independent and proportional to the dimensionless conductance, $g$, characterizing the 1d Luttinger liquid. Here $m$($<<M$) is the fermion mass, and $E_F$ is the Fermi energy. Below $T^{\ast }$, in the weak coupling regime, the mobility grows and diverges as $\mu (T)\sim T^{-4}$ in $T\to 0$ limit.

6 pages, RevteX, UCR

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