Mobility And Diffusion Of A Particle Coupled To A Luttinger Liquid

We study the mobility of a particle coupled to a one-dimensional interacting fermionic system, namely, a Luttinger liquid. We bosonize the Luttinger liquid and find the effective interaction between the particle and the bosonic system. We show that the dynamics of this system is completely equivalent to the acoustic polaron problem where the interaction has purely electronic origin. This problem has a zero-mode excitation, or soliton, in the strong-coupling limit, which corresponds to the the formation of a polarization cloud due to the fermion-fermion interaction around the particle. We find that, due to the scattering of the residual bosonic modes, the soliton has a finite mobility and diffusion coefficient at finite temperatures that depend on the fermion-fermion interaction. We show that at low temperatures the mobility and the diffusion coefficient are proportional to T-4 and T5, respectively, and at high temperatures the mobility vanishes as T-1 while the diffusion increases as T. © 1994 The American Physical Society.5074863486