Exact time-evolving resonant states for open double quantum-dot systems with spin degrees of freedom
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| Format: | Preprint |
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2025
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| _version_ | 1866910051231334400 |
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| author | Nishino, Akinori Hatano, Naomichi |
| author_facet | Nishino, Akinori Hatano, Naomichi |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_22195 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exact time-evolving resonant states for open double quantum-dot systems with spin degrees of freedom Nishino, Akinori Hatano, Naomichi Mesoscale and Nanoscale Physics Mathematical Physics Quantum Physics 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. |
| title | Exact time-evolving resonant states for open double quantum-dot systems with spin degrees of freedom |
| topic | Mesoscale and Nanoscale Physics Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2510.22195 |