| Budget Amount *help |
¥3,000,000 (Direct Cost: ¥3,000,000)
Fiscal Year 2005: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2004: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2003: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2002: ¥800,000 (Direct Cost: ¥800,000)
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| Research Abstract |
To clarify the static and dynamic properties of the Bose-Einstein condensates of ultra-cold neutral bosonic atoms, the following subjects were investigated.
1. Quantum delta-function gases
For one-dimensional quantum integrable particle systems, quasi-momentum distribution and excitation energy spectrum are described by Lieb-Liniger (LL) integral equation and Yang-Yang (YY) integral equation, respectively. Those integral equations are usually solved numerically, but the analytic work are few. In particular, the weak coupling case is known to be a hard problem. We apply the power-series expansion method for analysis of spin-1/2 fermion system where two kinds of fermions (spin up and spin down) interact through the attractive delta-function potential. In the strong coupling region, spin-pair states are shown to exist. This implies the occurrence of BCS state in ultra-cold gases.
2. Matter-wave propagations in F=1 spinor BEC condensate.
In optical trap, the condensates with internal degrees of freedom are realized. It was found that, when the magnitudes of inter-atomic potential and spin-exchange interaction are same, three-component Gross-Pitaevskii (GP) equation is integrable. Through the inverse scattering method, N-soliton solutions are obtained. For the attractive case, bright solitons exist and those are classified into polar soliton and ferromagnetic soliton. For the repulsive case, the similar results hold (in preparation). For general two coupling constants, matter-wave propagations are investigated. From the analysis of plane-wave solutions, we can show the existence of polar soliton and ferromagnetic soliton.
Since this year is the final year of the project, we extended analyses to the subjects such as soliton equations in non-commutative space-time, transports in one-dimensional exclusion processes and, geometric phases and quantum entanglements of two spins in a magnetic field.
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