Occupation of a resonant level coupled to a chiral Luttinger liquid

We consider a resonant level coupled to a chiral Luttinger liquid which can be realized, e.g., at a fractional quantum Hall edge. We study the dependence of the occupation probability n of the level on its energy \epsilon for various values of the Luttinger-liquid parameter g. At g<1/2 a weakly coupled level shows a sharp jump in n(\epsilon) at the Fermi level. As the coupling is increased, the magnitude of the jump decreases until \sqrt{2g}, and then the discontinuity in n(\epsilon) disappears. We show that n(\epsilon) can be expressed in terms of the magnetization of a Kondo impurity as a function of magnetic field.Comment: 5 pages including 1 figur

Decay of Bogoliubov excitations in one-dimensional Bose gases

We study the decay of Bogoliubov quasiparticles in one-dimensional Bose gases. Starting from the hydrodynamic Hamiltonian, we develop a microscopic theory that enables one to systematically study both the excitations and their decay. At zero temperature, the leading mechanism of decay of a quasiparticle is disintegration into three others. We find that low-energy quasiparticles (phonons) decay with the rate that scales with the seventh power of momentum, whereas the rate of decay of the high-energy quasiparticles does not depend on momentum. In addition, our approach allows us to study analytically the quasiparticle decay in the whole crossover region between the two limiting cases. When applied to integrable models, including the Lieb-Liniger model of bosons with contact repulsion, our theory confirms the absence of the decay of quasiparticle excitations. We account for two types of integrability-breaking perturbations that enable finite decay: three-body interaction between the bosons and two-body interaction of finite range.Comment: 17 page

Thermal conductivity of the degenerate one-dimensional Fermi gas

We study heat transport in a gas of one-dimensional fermions in the presence of a small temperature gradient. At temperatures well below the Fermi energy there are two types of relaxation processes in this system, with dramatically different relaxation rates. As a result, in addition to the usual thermal conductivity, one can introduce the thermal conductivity of the gas of elementary excitations, which quantifies the dissipation in the system in the broad range of frequencies between the two relaxation rates. We develop a microscopic theory of these transport coefficients in the limit of weak interactions between the fermions.Comment: 17 page