We develop a kinetic theory for strongly correlated disordered one-dimensional electron systems out of equilibrium within the Luttinger liquid model. In the absence of inhomogeneities, the model exhibits no relaxation to equilibrium. We derive kinetic equations for electron and plasmon distribution functions in the presence of impurities and calculate the equilibration rate ${\ensuremath{\gamma}}_{E}$. Remarkably, for not too low temperature and bias voltage, ${\ensuremath{\gamma}}_{E}$ is given by the elastic backscattering rate $\ensuremath{\gamma}$: the ratio ${\ensuremath{\gamma}}_{E}/\ensuremath{\gamma}\ensuremath{\sim}1$ is independent of the strength of electron-electron interaction, temperature, and bias.We develop a kinetic theory for strongly correlated disordered one-dimensional electron systems out of equilibrium within the Luttinger liquid model. In the absence of inhomogeneities, the model exhibits no relaxation to equilibrium. We derive kinetic equations for electron and plasmon distribution functions in the presence of impurities and calculate the equilibration rate ${\ensuremath{\gamma}}_{E}$. Remarkably, for not too low temperature and bias voltage, ${\ensuremath{\gamma}}_{E}$ is given by the elastic backscattering rate $\ensuremath{\gamma}$: the ratio ${\ensuremath{\gamma}}_{E}/\ensuremath{\gamma}\ensuremath{\sim}1$ is independent of the strength of electron-electron interaction, temperature, and bias.

arXiv:0809.3166Physical Review BSep 21, 200915 citations

Theory of Nonlinear Luttinger Liquids

L. I. Glazman

Bulletin of the American Physical SocietyMar 16, 20100 citations

Landauer transport theory for Luttinger liquids

Reinhold Egger, Hermann Grabert

Jan 1, 20000 citations

Relaxation processes in a disordered Luttinger liquid

Д. А. Багрец, I. V. Gornyi, A. D. Mirlin +1 more

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 a 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 a 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 a 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 on the order of the rate of elastic scattering off disorder, independent of the interaction constant and temperature.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 a 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 a 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 a 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 on the order of the rate of elastic scattering off disorder, independent of the interaction constant and temperature.

arXiv:0804.4887SemiconductorsAug 1, 200816 citations

Transport in Luttinger Liquids

Thierry Giamarchi, Thomas Nattermann, Pierre Le Doussal

Springer eBooksJan 1, 20040 citations

$U(1)$ Fermi liquid theory - A Fermi liquid state that supports exclusion statistics$U(1)$ Fermi liquid theory - A Fermi liquid state that supports exclusion statistics

Tai Kai Ng

We propose in this paper an effective low-energy theory for interacting fermion systems which supports exclusion statistics. The theory can be viewed as an extension of Landau Fermi liquid theory where besides quasi-particle energy $ξ_{\mathbf{k}}$ , the kinetic momentum $\mathbf{k}$ of quasi-particles depends also on quasi-particle occupation numbers as a result of momentum ( $k$ )-dependent current-current interaction. The dependence of kinetic momentum on quasi-particles excitations leads to change in density of states and exclusion statistics. The properties of this new Fermi liquid state is studied where we show that the state (which we call $U(1)$ -Fermi liquid state) has Fermi-liquid like properties except that the quasi-particles are {\em not} adiabatically connected to bare fermions in the system and the state may not satisfy Luttinger theorem.We propose in this paper an effective low-energy theory for interacting fermion systems which supports exclusion statistics. The theory can be viewed as an extension of Landau Fermi liquid theory where besides quasi-particle energy $ξ_{\mathbf{k}}$, the kinetic momentum $\mathbf{k}$ of quasi-particles depends also on quasi-particle occupation numbers as a result of momentum ($k$)-dependent current-current interaction. The dependence of kinetic momentum on quasi-particles excitations leads to change in density of states and exclusion statistics. The properties of this new Fermi liquid state is studied where we show that the state (which we call $U(1)$-Fermi liquid state) has Fermi-liquid like properties except that the quasi-particles are {\em not} adiabatically connected to bare fermions in the system and the state may not satisfy Luttinger theorem.

arXiv:1610.08633Oct 27, 20160 citations

U(1)

Fermi liquid theory - A Fermi liquid state that supports exclusion statistics

ξ_{\mathbf{k}}

, the kinetic momentum

\mathbf{k}

of quasi-particles depends also on quasi-particle occupation numbers as a result of momentum (

k

)-dependent current-current interaction. The dependence of kinetic momentum on quasi-particles excitations leads to change in density of states and exclusion statistics. The properties of this new Fermi liquid state is studied where we show that the state (which we call

U(1)

-Fermi liquid state) has Fermi-liquid like properties except that the quasi-particles are {\em not} adiabatically connected to bare fermions in the system and the state may not satisfy Luttinger theorem.