Resonance in an open quantum dot system with a Coulomb interaction: a Bethe-ansatz approach

The purpose of this letter is to observe resonance in an open quantum system with a Coulomb interaction. The system that we study is the two-lead interacting resonant-level model (IRLM), which consists of two leads of non-interacting electrons that interact with an electron on a quantum dot in between the two leads. We obtain N -electron scattering states for arbitrary N , generalizing the Bethe-ansatz approach to open systems. By using the scattering states, we exactly calculate the quantum-mechanical expectation value of the electric current through the quantum dot, thereby observing resonance peaks. Some of the resonance peaks appear only when the interaction exists; they reflect the effect of many-body scattering. The resonance of many-body scattering that we observe in the quantum-mechanical expectation value has not been found in previous works with the Bethe ansatz. The Bethe-ansatz approach has provided a nonperturbative method of studying equilibrium states of interacting quantum systems including the Kondo problem.1–5 The approach is now used to discuss transport properties of mesoscopic systems. Konik et al.6,7 studied transport properties of the Anderson model in the thermodynamic limit of a closed system with periodic boundary conditions. Our scattering states, in contrast, appear only in open systems; they are constructed without imposing periodic boundary conditions. By extending the Bethe-ansatz approach, Mehta and Andrei8 studied the two-lead IRLM as an open system to obtain N -electron scattering states giving nonequilibrium steady states in the limit N → ∞. In their study, however, the quantum-mechanical expectation value of the current does not depend on the interaction; the effect of the interaction appears only in the statistical-mechanical expectation value as modification of the Fermi distribution in the leads. Thus our results are different from the previous ones.