Dynamics of a heavy particle in a Luttinger liquid.

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 comoving 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*5(m/M )EF , the particle’s mobility m is found to be ~roughly! temperature independent and proportional to the dimensionless conductance g , characterizing the one-dimensional Luttinger liquid. Here m(!M ) is the fermion mass, and EF the Fermi energy. Below T*, in the weak-coupling regime, the mobility grows and diverges as m(T);T in the T→0 limit.