Exact Scattering Eigenstates, Many-Body Bound States, and Nonequilibrium Current in an Open Quantum Dot System

Abstract

We obtain an exact many-body scattering eigenstate in an open quantum dot system. The scattering state is not in the form of the Bethe eigenstate in the sense that the wave-number set of the incoming plane wave is not conserved during the scattering and many-body bound states appear. By using the scattering state, we study the average nonequilibrium current through the quantum dot under a finite bias voltage. The current-voltage characteristics that we obtained by taking the two-body bound state into account is qualitatively similar to several known results.

Waveguide QED: Many-body bound-state effects in coherent and Fock-state scattering from a two-level system

“…As discussed by Shen and Fan [18,19], a two-photon bound state must be included to guarantee the completeness of the basis. Here, instead of extracting the bound state through a completeness check [18,19], we construct the scattering eigenstate explicitly and find a two-photon boundstate contribution to the solution, as has been done in the open interacting resonant-level model [21]. We require the two-photon solution to satisfy Eq.…”

“…. ,n. In all the following calculations, we set g n (0, [21,22]. The scattering eigenstates g n (x 1 , .…”

“…1. First, we explicitly construct the n-photon (n = 1 to 4) scattering eigenstates by imposing open boundary conditions while requiring that the incoming wave functions consist entirely of plane waves [21,22]. In addition to two-photon bound states, three-photon bound states appear in the three-photon scattering eigenstates, and likewise, n-photon bound states appear in the n-photon scattering eigenstates.…”

Real-time simulations of nonequilibrium transport in the single-impurity Anderson model

“…However, the understanding of open systems out of equilibrium remains an extremely challenging area of research. While recent studies have succeeded in calculating the currentvoltage (I-V) characteristics of the interacting resonant level model, 4,5,6,7,8 the focus of current research has been devoted toward the more difficult single-impurity Anderson model incorporating Kondo correlations. For example, experimental results for the finite-bias transport properties of a quantum dot still await a complete theoretical explanation.…”

Interacting resonant-level model with long-range interactions: Fast screening and suppression of the zero-bias conductance

“…Recently, a short-range (SR) dot-lead interaction has been shown to reduce the quasiparticle gap in equilibrium [4][5][6][7] and to reopen it at sufficiently large biases. 8 In the interacting resonant level model (IRLM) the SR interaction is also at the origin of a negative differential conductance with an interaction-dependent power-law decay [9][10][11][12] as well as of an overall enhancement of the off-resonance conductance. 13,14 In recent years the experimental progress in producing low-dimensional conducting wires has been accompanied by an increasing number of theoretical studies on the IRLM with single-channel leads.…”