Equilibration of a one-dimensional quantum liquid

We review some of the recent results on equilibration of one-dimensional quantum liquids. The low-energy properties of these systems are described by the Luttinger liquid theory, in which the excitations are bosonic quasiparticles. At low temperatures the relaxation of the gas of excitations toward full equilibrium is exponentially slow. In electronic Luttinger liquids these relaxation processes involve backscattering of electrons and give rise to interesting corrections to the transport properties of one-dimensional conductors. We focus on the phenomenological theory of the equilibration of a quantum liquid and obtain an expression for the relaxation rate in terms of the excitation spectrum

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

Quantum criticality in a double quantum-dot system

We discuss the realization of the quantum-critical non-Fermi liquid state, originally discovered within the two-impurity Kondo model, in double quantum-dot systems. Contrary to the common belief, the corresponding fixed point is robust against particle-hole and various other asymmetries, and is only unstable to charge transfer between the two dots. We propose an experimental set-up where such charge transfer processes are suppressed, allowing a controlled approach to the quantum critical state. We also discuss transport and scaling properties in the vicinity of the critical point.Comment: 4 pages, 3 figs; (v2) final version as publishe

Shifts of Random Energy Levels by a Local Perturbation

We consider the effect of a local perturbation on the energy levels of a system described by random matrix theory. An analytic expression for the joint distribution function of initial and final energy levels is obtained. In the case of unitary ensemble we also find the two-point correlation function of initial and final densities of states.Comment: 4 page