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We consider a model of quantum-wire junctions where the latter are describedby conformal-invariant boundary conditions of the simplest type in themulticomponent compactified massless scalar free field theory representing thebosonized Luttinger liquids in the bulk of wires. The boundary conditionsresult in the scattering of charges across the junction with nontrivialreflection and transmission amplitudes. The equilibrium state of such a system,corresponding to inverse temperature $\beta$ and electric potential $V$, isexplicitly constructed both for finite and for semi-infinite wires. In thelatter case, a stationary nonequilibrium state describing the wires kept atdifferent temperatures and potentials may be also constructed. The main resultof the present paper is the calculation of the full counting statistics (FCS)of the charge and energy transfers through the junction in a nonequilibriumsituation. Explicit expressions are worked out for the generating function ofFCS and its large-deviations asymptotics. For the purely transmitting case theycoincide with those obtained in the litterature, but numerous cases ofjunctions with transmission and reflection are also covered. The largedeviations rate function of FCS for charge and energy transfers is shown tosatisfy the fluctuation relations and the expressions for FCS obtained here arecompared with the Levitov-Lesovic formulae.

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