| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Outline of Final Research Achievements |
The spectrum of the discrete Lalacian on a graph describes the energy of a free particle moving in a substance and the Bose-Einstein condensation is a phenomenon that a macroscopic number of particles occupy the lowest energy state. In this case, the graph represents the structure of the substance. In this study, we have clarified the relation between the spectra of the Laplacians on infinite graphs and the shapes of the graphs. We have also given examples of graphs where BEC occurs. As by-products, we have revealed the structure of the discrete Schroedinger operator consisting of the Laplacian and an interaction term and that of a quantum walk, which is a quantum mechanical counterpart of a random walk. Moreover, we have proved the weak limit theorem, which gives the long-time limit distribution of the quantum walk.
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