| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2017: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Outline of Final Research Achievements |
The spectral structures in the quantum Rabi model and the asymmetric quantum Rabi model are fully described. Representation theoretical characterization of degenerate and non-degenerate eigenvalues was also obtained. We have studied the similarity of the Aperi numbers that appears from special values of the spectral zeta function of non-commutative harmonic oscillators. In addition to getting some notable congruential relations, we obtained some interesting conjectures. We also show the explicit expression of those generating functions at s=4 by a generalization of the automorphic integrals. We also investigated related cohomology groups and Hecke operators. An analytical formula for the heat kernel of the quantum Rabi model was obtained. Specifically, like the Kondo effect correlation function, the heat kernel is described as an infinite series of iterative integrals. This gives also the partition function and the explicit analytic continuation of the spectral zeta function.
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