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Transport of a Luttinger liquid in the presence of a time dependent impurity

D. Schmeltzer
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Abstract

We show that the macroscopic current and charge can be formulated as a Quantum Mechanical zero mode problem. We find that the current is given by the velocity operator of a particle restricted to move around a circle. As an explicit example we investigate a Luttinger liquid of length $L$ which is perturbed by a time dependent impurity. Using the statistical mechanics of zero modes we computed the non-equilibrium current. In particular we show that in the low temperature limit, $L_T/L>1$, the zero mode method introduced here becomes essential for computing the current.

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D. Schmeltzer. 2000-11-21. Transport of a Luttinger liquid in the presence of a time dependent impurity. https://doi.org/10.1103/physrevb.63.125332

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