Nonequilibrium transport through quantum-wire junctions and boundary defects for free massless bosonic fields

TL;DR

This paper models quantum-wire junctions using conformal boundary conditions in free bosonic fields, explicitly constructing equilibrium and nonequilibrium states, and calculating full counting statistics of charge and energy transfers, including reflection and transmission effects.

Contribution

It provides explicit formulas for full counting statistics in quantum-wire junctions with complex boundary conditions, extending previous results to include reflection and transmission.

Findings

Explicit FCS generating functions derived for various junction configurations.

Large deviations rate functions satisfy fluctuation relations.

Results generalize Levitov-Lesovic formulae to more complex junctions.

Abstract

We consider a model of quantum-wire junctions where the latter are described by conformal-invariant boundary conditions of the simplest type in the multicomponent compactified massless scalar free field theory representing the bosonized Luttinger liquids in the bulk of wires. The boundary conditions result in the scattering of charges across the junction with nontrivial reflection and transmission amplitudes. The equilibrium state of such a system, corresponding to inverse temperature $\beta$ and electric potential $V$, is explicitly constructed both for finite and for semi-infinite wires. In the latter case, a stationary nonequilibrium state describing the wires kept at different temperatures and potentials may be also constructed. The main result of the present paper is the calculation of the full counting statistics (FCS) of the charge and energy transfers through the junction in a nonequilibrium situation. Explicit expressions are worked out for the generating function of FCS and its large-deviations asymptotics. For the purely transmitting case they coincide with those obtained in the litterature, but numerous cases of junctions with transmission and reflection are also covered. The large deviations rate function of FCS for charge and energy transfers is shown to satisfy the fluctuation relations and the expressions for FCS obtained here are compared with the Levitov-Lesovic formulae.