The mobility and diffusion of a particle coupled to a Luttinger liquid

Abstract

We study the mobility of a particle coupled to a one dimensional interacting fermionic system, 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 formation of a polarization cloud due to the fermion-fermion interaction around the particle. We obtain that, due to the scattering of the residual bosonic modes, the soliton has a finite mobility and diffusion coefficient at finite temperatures which depend on the fermion-fermion interaction. We show that at low temperatures the mobility and the diffusion coefficient are proportional to $T^{-4}$ and $T^5$ respectively and at high temperatures the mobility vanishes as $T^{-1}$ while the diffusion increases as $T$.

9 pages, Revtex, UIUC preprint

References in corpus (4)

• Bosonization of Fermi liquids
• Exact calculation of spectral properties of a particle interacting with a one dimensional fermionic system
• An alternative approach for the dynamics of polarons in one dimension
• Transport Properties of Solitons

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• Dynamics of a heavy particle in a Luttinger liquid
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• Kondo polarons in a one-dimensional Fermi gas
• Ponderous impurities in a Luttinger liquid
• Selected Topics in the Theory of 1D Quantum Wires
• The double Caldeira-Leggett model: Derivation and solutions of the master equations, reservoir-induced interactions and decoherence
• Mobile impurities in integrable models
• Mobility of Bloch Walls via the Collective Coordinate Method
• Over forty years of research towards the understanding of Quantum Brownian Motion -- the contributions of A. O. Caldeira