2001 Fiscal Year Final Research Report Summary
Nonlinear analysis of Bose-Einstein Condensates
| Project/Area Number |
11640387
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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 |
物理学一般
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| Research Institution | The University of Tokyo |
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Principal Investigator |
WADATI Miki The University of Tokyo, Graduate School of Science, Professor, 大学院・理学系研究科, 教授 (60015831)
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| Project Period (FY) |
1999 – 2001
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| Keywords | Nonlinear Schrodinger equation / Bose-Einstein condensate / 2-conponent Bosonic atoms / Stability of condensate / Gross-Pitaeyskii equation / Free fall / Toroidal trap / One-dimensional δ-function gas |
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| Research Abstract |
1.In the case that the effective interaction between atoms is attractive, the condensate becomes unstable when the number of atoms exceeds some value (critical particle number). Using a new inequality, we discussed rigorously the stability condition of Gross-Pitaevskii equation (Nonlinear Schroedinger equation).
2.We analyzed the Bose-Einstein condensate under a troidal trap. In Particular, we clarified the ground state properties the ground state energy decreases and the distribution of atoms is shifted to the central axis.
3.For the dispersion relation E〜k^a. we investigated the condition of the condensation. By using the WKB method, we found the relation between the dispersion relation and the power-law of the magnetic trap V〜r^p. When the potential decreases rapidly around r=0, we pointed out that the Bose-Einstein condensation takes place even in one dimension. Also, we showed that the values of a and p change drastically the properties of the transition.
4.We analyzed the free tall of the condensate including the atomic interactions. Interference patterns of atomic waves reflect the interactions, which are observable in experiments.
5.We developed a statistical mechanics of one-dimensional delta function gas. By the peturbational method, we derived the integral equation of thermal Bethe ansatz equation. This is a fisrt direct proof of the Bethe anasatz.
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