Exact time-evolving scattering states in open quantum-dot systems with an interaction: Discovery of time-evolving resonant states

Abstract

We study exact time-evolving many-electron states of an open double quantum-dot system with an interdot Coulomb interaction. A systematic construction of the time-evolving states for arbitrary initial conditions is proposed. For any initial states of one- and two-electron plane waves on the electrical leads, we obtain exact solutions of the time-evolving scattering states, which converge to known stationary scattering eigenstates in the long-time limit. For any initial states of localized electrons on the quantum dots, we find exact time-evolving states of a new type, which we refer to as time-evolving resonant states. In contrast to stationary resonant states, whose wave functions spatially diverge and not normalizable, the time-evolving resonant states are normalizable since their wave functions are restricted to a finite space interval due to causality. The exact time-evolving resonant states enable us to calculate the time-dependence of the survival probability of electrons on the quantum dots for the system with the linearized dispersions. It decays exponentially in time on one side of an exponential point of resonance energies while, on the other side, it oscillates during the decay as a result of the interference of the two resonance energies.

31 pages, 5 figures

References in corpus (22)

• Kondo Physics in a Single Electron Transistor
• A Tunable Kondo Effect in Quantum Dots
• Low Temperature Transport through a Quantum Dot: The Anderson Model out of Equilibrium
• The Kondo Effect in the Unitary Limit
• The Anderson Model out of Equilibrium: Non-Crossing-Approximation Approach to Transport through a Quantum Dot
• Transport Coefficients of the Anderson Model via the Numerical Renormalization Group
• Twofold advance in the theoretical understanding of far-from-equilibrium properties of interacting nanostructures
• Interference Effects on Kondo-Assisted Transport through Double Quantum Dots
• Some properties of the resonant state in quantum mechanics and its computation
• Non-equilibrium current and relaxation dynamics of a charge-fluctuating quantum dot
• New method for studying steady states in quantum impurity problems: The interacting resonant level model
• Exact scattering eigenstates, many-body bound states, and nonequilibrium current of an open quantum dot system
• Non-Markovian dynamics revealed at the bound state in continuum
• Amplification of non-Markovian decay due to bound state absorption into continuum
• Power law tails and non Markovian dynamics in open quantum systems: An exact solution from Keldysh field theory
• Single-electron approach for time-dependent electron transport
• Shot noise in the interacting resonance level model
• Universal electric current of interacting resonant-level models with asymmetric interactions: An extension of the Landauer formula
• Time-Reversal Symmetry and Arrow of Time in Quantum Mechanics of Open Systems
• Many-body wavefunctions for quantum impurities out of equilibrium. I. The nonequilibrium Kondo model
• Many-body wavefunctions for quantum impurities out of equilibrium
• Many-body wavefunctions for quantum impurities out of equilibrium. II. Charge fluctuations