DYNAMICS OF A HEAVY-PARTICLE IN A LUTTINGER LIQUID

We study the dynamics of a heavy particle of mass M moving in a one-di mensional repulsively interacting Fermi gas. The Fermi gas is describe d using the Luttinger model and bosonization. By transforming to a fra me comoving with the heavy particle, we map the model onto a generaliz ed ''quantum impurity problem.'' A renormalization-group calculation r eveals a crossover from strong to weak coupling upon scaling down in t emperature. Above the crossover temperature scale T=(m/M)E(F), the pa rticle's mobility mu is found to be (roughly) temperature independent and proportional to the dimensionless conductance g, characterizing th e one-dimensional Luttinger liquid. Here m(much less than M) is the fe rmion mass, and E(F) the Ferni energy. Below T, in the weak-coupling regime, the mobility grows and diverges as mu(T)similar to T-4 in the T-->0 limit.