| Project/Area Number |
22K03473
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 13010:Mathematical physics and fundamental theory of condensed matter physics-related
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| Research Institution | Osaka Metropolitan University |
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Principal Investigator |
ガーモン サバンナスターリング 大阪公立大学, 大学院理学研究科, 准教授 (30733860)
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| Project Period (FY) |
2022-04-01 – 2025-03-31
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| Project Status |
Granted (Fiscal Year 2023)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2024: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2023: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2022: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | exceptional point / microscopic dynamics / structured reservoir / weak-coupling states / non-Markovian dynamics / Liouvillian / topological insulator / Lindblad / Exceptional point / Lindblad operator / non-Hermitian physics / quantum jump |
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| Outline of Research at the Start |
This proposal has three main objectives that will be implemented consecutively as follows.
1) I will analyze the influence of quantum jump processes on two basic types of EPs, one involving the appearance of a resonance and one involving the coalescence of two existing resonances.
2) Extend the analysis to the case of an anomalous-order EP occurring directly at the continuum threshold in certain 1-D systems
3) Develop a general theory for dynamics near exceptional points in quantum systems accounting for quantum jump processes.
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| Outline of Annual Research Achievements |
I have made progress on two tracks related to the dynamics at the exceptional point (EP). The original intention was to study the dynamics at the EP at the level of the Liouvillian based on the Lindblad operator formalism. However, the first track focuses on the dynamics at the Hamiltonian level.
(1) I have continued my studies on the semi-infinite Su-Schrieffer-Heeger (SSH) model with an attached quantum emitter. I have found that in the topologically non-trivial phase of the SSH reservoir, two unique parameter regimes appear with non-conventional physics. In one of these regimes, a pair of bound states appears for weak coupling. (Normally, bound states only appear in the strong coupling regime.) Further, an exceptional point separates the regime of non-conventional physics from the conventional regime. We have obtained an analytic approximation for the dynamics in this case that demonstrates both Markovian and non-Markovian dynamics.
(2) I have come to realize that Lindblad formalism probably can't be applied to the dynamics of a true open quantum system because Lindblad is a Markovian procedure while the open system necessarily introduces non-Markovian dynamics. Hence I have instead begun a project studying the dynamics in a Liouvillian system working from first principles. This is a challenging project and it is still in the early stages, but it seems quite promising.
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| Current Status of Research Progress |
Current Status of Research Progress
3: Progress in research has been slightly delayed.
Reason
The project is a bit delayed because the focus has changed somewhat. The calculation of the Liouviliian dynamics under track (2) is much more challenging than the original objective, but should yield interesting results.
Then under track (1) the calculation of the dynamics at the exceptional point in the topologically non-trivial SSH chain has proved challenging as well, but we have finally obtained a solution. We are presently writing a paper to present these results.
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| Strategy for Future Research Activity |
Under track (1), I will analyze the dynamics at the pair of bound states appearing in the weak coupling regime. In the case of wide separation of the bound states from the band edges of the two SSH bands, this should result in an anomalous regime of sub-radiant dynamics. In the case that the bound states approach the edges of the SSH bands, according to my previous works [Garmon, 2013] this should induce non-Markovian dynamics.
Under track (2), I will establish the formalism needed to analyze the dynamics at an open quantum system without employing a Markovian approximation.
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