Numerical analysis of the spectrum of large finite size Luttinger liquids $(g<1)$ in the presence of a single source of ${2k}_{f}$ scattering has been made possible due to an effective integration of high degrees of freedom. The presence of irrelevant operators and their manifestation in transport are issues treated independently. We confirm the existence of two irrelevant operators: particle hopping and charge oscillations, with regions of dominance separated by $g\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2$ . Temperature dependence of conductance is shown to be controlled by hopping alone, giving $G\ensuremath{\sim}{T}^{2/g\ensuremath{-}2}$. Frequency dependence is affected by both operators, giving $G\ensuremath{\sim}{\ensuremath{\omega}}^{2/g\ensuremath{-}2}$ for $g>1/2$ , and $G\ensuremath{\sim}{\ensuremath{\omega}}^{2}$ for $g<1/2$ .Numerical analysis of the spectrum of large finite size Luttinger liquids $(g<1)$ in the presence of a single source of ${2k}_{f}$ scattering has been made possible due to an effective integration of high degrees of freedom. The presence of irrelevant operators and their manifestation in transport are issues treated independently. We confirm the existence of two irrelevant operators: particle hopping and charge oscillations, with regions of dominance separated by $g\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2$. Temperature dependence of conductance is shown to be controlled by hopping alone, giving $G\ensuremath{\sim}{T}^{2/g\ensuremath{-}2}$. Frequency dependence is affected by both operators, giving $G\ensuremath{\sim}{\ensuremath{\omega}}^{2/g\ensuremath{-}2}$ for $g>1/2$, and $G\ensuremath{\sim}{\ensuremath{\omega}}^{2}$ for $g<1/2$.

arXiv:cond-mat/9508013Physical Review LettersMay 27, 199614 citations

Landauer transport theory for Luttinger liquids

Reinhold Egger, Hermann Grabert

Jan 1, 20000 citations

Transient effects in the backscattered current of a Luttinger liquid

Mariano J. Salvay, Hugo Aita, Carlos Naón

We study the backscattered current in a Luttinger liquid in the presence of a pointlike weak impurity switched on at finite time, taking into account finite-temperature effects. We show how the well-known results for a static impurity are distorted. We derive a dimensionless parameter ${\ensuremath{\tau}}_{R}$ as a function of the electron-electron interaction and the temperature, such that for ${\ensuremath{\tau}}_{R}<1$ $(>1)$ the switching process is relevant (irrelevant). Our results suggest the possibility of determining the value of the Luttinger parameter $K$ through time measurements in transport experiments at fixed voltage.We study the backscattered current in a Luttinger liquid in the presence of a pointlike weak impurity switched on at finite time, taking into account finite-temperature effects. We show how the well-known results for a static impurity are distorted. We derive a dimensionless parameter ${\ensuremath{\tau}}_{R}$ as a function of the electron-electron interaction and the temperature, such that for ${\ensuremath{\tau}}_{R}<1$ $(>1)$ the switching process is relevant (irrelevant). Our results suggest the possibility of determining the value of the Luttinger parameter $K$ through time measurements in transport experiments at fixed voltage.

arXiv:1002.3121Physical Review BMar 5, 20107 citations

Transport in Luttinger Liquids

Thierry Giamarchi, Thomas Nattermann, Pierre Le Doussal

Jan 1, 20040 citations

Numerical analysis of the spectrum of large finite size Luttinger liquids

(g<1)

in the presence of a single source of

{2k}_{f}

scattering has been made possible due to an effective integration of high degrees of freedom. The presence of irrelevant operators and their manifestation in transport are issues treated independently. We confirm the existence of two irrelevant operators: particle hopping and charge oscillations, with regions of dominance separated by

g\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2

. Temperature dependence of conductance is shown to be controlled by hopping alone, giving $G\ensuremath{\sim}{T}^{2/g\ensuremath{-}2}$. Frequency dependence is affected by both operators, giving $G\ensuremath{\sim}{\ensuremath{\omega}}^{2/g\ensuremath{-}2}$ for

g>1/2

, and $G\ensuremath{\sim}{\ensuremath{\omega}}^{2}$ for

g<1/2

(>1)

the switching process is relevant (irrelevant). Our results suggest the possibility of determining the value of the Luttinger parameter

K

through time measurements in transport experiments at fixed voltage.