Relaxation processes in a disordered Luttinger liquid

Details Relaxation processes in a disordered Luttinger liquid Relaxation processes in a disordered Luttinger liquid

2008-04-30

arxiv.org/abs/0804.4887v1

Semiconductors 42, 994 (2008)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

13 pages, 2 figures; contribution to a special issue of "Semiconductors" dedicated to V.I. Perel

Scientific paper

10.1134/S1063782608080204

The Luttinger liquid model, which describes interacting electrons in a single-channel quantum wire, is completely integrable in the absence of disorder and as such does not exhibit any relaxation to equilibrium. We consider relaxation processes induced by inelastic electron-electron interactions in a disordered Luttinger liquid, focusing on the equilibration rate and its essential differences from the electron-electron scattering rate as well as the rate of phase relaxation. In the first part of the paper, we review the basic concepts in the disordered Luttinger liquid at equilibrium. These include the elastic renormalization, dephasing, and interference-induced localization. In the second part, we formulate a conceptually important framework for systematically studying the nonequilibrium properties of the strongly correlated (non-Fermi) Luttinger liquid. We derive a coupled set of kinetic equations for the fermionic and bosonic distribution functions that describe the evolution of the nonequilibrium Luttinger liquid. Remarkably, the energy equilibration rate in the conducting disordered quantum wire (at sufficiently high temperature, when the localization effects are suppressed by dephasing) is shown to be of the order of the rate of elastic scattering off disorder, independent of the interaction constant and temperature.

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