| Project/Area Number |
17K05584
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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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| Research Field |
Mathematical physics/Fundamental condensed matter physics
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| Research Institution | Tokyo Metropolitan University |
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Principal Investigator |
Tanaka Atushi 首都大学東京, 理学研究科, 助教 (20323264)
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| Project Period (FY) |
2017-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 新奇な量子ホロノミー / 断熱定理 / 準位反転 / 量子状態制御 / 断熱サイクル / 量子古典対応 / 物性基礎論 / 量子論基礎 / フロケ系 |
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| Outline of Final Research Achievements |
We studied an application of exotic quantum holonomy to a "topological manipulation" of quantum states. In particular, we examined weakly interacting Bose particles confined in a one-dimensional region. We introduce a periodic operation, where the strength of impurity potential is varied adiabaticaly, except at a quench point where the strength diverges. When the interparticle interaction is weak enough, we confirmed that the exotic quantum holonomy really occurs. On the other hand, if the interparticle interaction exceeds a critical value, the exotic quantum holonomy is hindered due to the bifurcation of the stationary states.
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| Academic Significance and Societal Importance of the Research Achievements |
これまで、新規な量子ホロノミーは自由度の小さい量子系と、Lieb-Liniger模型と呼ばれる厳密可解な多体系を中心に調べられてきた。新奇な量子ホロノミーの存在は、熱力学的な系での断熱準静変化とミクロ量子系の断熱変化との決定的な違いの一つであり、近年の統計力学の基礎に関する研究の動向に関連した発展も期待される。また、本研究で扱かった一次元空間中で弱く相互作用するボーズ粒子系では実験的な研究との関連も期待される。実際、 dipolar Bose gas での新奇な量子ホロノミーノ実験が最近報告された (Kao et al., arXiv:2002.10475)。
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