| Project/Area Number |
16540347
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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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 | Osaka City University |
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Principal Investigator |
NAKAMURA Katsuhiro Osaka City University, Graduate School of Engineering, Professor, 大学院工学研究科, 教授 (50140801)
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| Co-Investigator(Kenkyū-buntansha) |
TERAI Akira Osaka City University, Graduate School of Engineering, Associate Professor, 大学院工学研究科, 助教授 (20192651)
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| Project Period (FY) |
2004 – 2006
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| Project Status |
Completed (Fiscal Year 2006)
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| Budget Amount *help |
¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2006: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2005: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2004: ¥1,500,000 (Direct Cost: ¥1,500,000)
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| Keywords | Bose-Einstein condensate(BEC) / Rabi oscillation / Billiard motion / Soliton in spatially 2 dimensions / Nonlinear dynamics / ボーズ・アインシュタイン凝縮体 / 調和型閉じ込めポテンシャル / 非線形シュレーディンガー方程式 / エルミートクラスター渦 / カオス / グロス=ピタエフスキー方程式 / BEC / 干渉問題 / 2重スリット / 非線形シュレディンガー方程式 / 重力の影響 / 巨視的波束 |
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| Research Abstract |
Bose-Einstein condensate(BEC) provides a nice stage when the nonlinear Schr{"o}dinger equation plays a vital role.
We study the dynamics of multi-component repulsive BEC in 2 dimensions with harmonic traps by using the nonlinear
Schr{"o}dinger (or Gross-Pitaevskii) equation.
Firstly we consider a driven two-component BEC with each component trapped in different vertical positions.
The appropriate tuning of the oscillation frequency of the magnetic field leads to a striking anti-gravity transport of BEC. This phenomenon is a manifestation of macroscopic non-adiabatic tunneling in a system with two internal(electronic) degrees of freedom.
The dynamics splits into a fast complex spatio-temporal oscillation of each condensate wavefunctions together with a slow levitation of the total center of mass.
Secondly, we examine the three-component repulsive BEC in 2 dimensions in a harmonic trap in the absence of magnetic field, and construct a model of conservative chaos based on a picture of vortex molecules.
We obtain an effective nonlinear dynamics for three vortex cores,
which represents three charged particles under the uniform magnetic field with the repulsive inter-particle potential quadratic in the inter-vortex distance $r_{ij}$ on short scale and logarithmic in $r_{ij}$ on large scale. The vortices here acquire the inertia in marked contrast to the standard theory of point vortices since Onsager.
We then explore "the chaos in the three-body problem" in the context of vortices with inertia.
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