Exact time-evolving resonant states for open double quantum-dot systems with spin degrees of freedom

TL;DR

This paper derives an exact non-Hermitian Hamiltonian for open double quantum-dot systems with spin, identifying resonant states and solving the time-dependent Schrödinger equation to analyze electron dynamics.

Contribution

It introduces a precise method to analyze time-evolving resonant states in open quantum-dot systems with spin and Coulomb interactions, including an exact solution for the dynamics.

Findings

Identified four types of two-body resonant states.

Derived an exact non-Hermitian effective Hamiltonian.

Solved the time-dependent Schrödinger equation for localized electrons.

Abstract

We study time-evolving resonant states in an open double quantum-dot system, taking into account spin degrees of freedom as well as both on-dot and interdot Coulomb interactions. We exactly derived a non-Hermite effective Hamiltonian acting on the subspace of two quantum dots, where the non-Hermiticity arises from an effect of infinite external leads connected to the quantum dots. By diagonalizing the effective Hamiltonian, we identify four types of two-body resonant states. For the initial states of localized two electrons with opposite spins on the quantum dots, we exactly solve the time-dependent Schroedinger equation and obtain time-evolving two-body resonant states. The time-evolving resonant states are normalizable since their wave function grows exponentially only inside a finite space interval that expands in time with electron velocity. By using the exact solution, we analyze the survival and transition probabilities of localized two electrons on the quantum dots.