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DAN Yuya
Department Matsuyama University Department of Business Administration, Faculty of Business Administration Position Professor |
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| Language | Japanese |
| Publication Date | 2013/08 |
| Type | |
| Title | Mathematical Analysis for Quantum Complex Systems |
| Contribution Type | |
| Journal | Matsuyama University Review |
| Publisher | Matsuyama University |
| Volume, Issue, Pages | 67-98頁 |
| Details | This article is composed of the historical and recent results in stability of quantum complex systems using mathematical approaches.
It is important to treat the problem rigorously and compute the accurate values we estimate mathematically. We mainly consider Schr\"o\-dinger operators and the pseudo-relativistic operators with electric and magnetic interaction in Euclidean spaces with various inequalities in spectral theory, in order to estimate the ground state energy of quantum complex systems. According to the concept of the second kind of stability, we can prove the stability in almost all realistic settings we always consider. It is also discussed that Pauli and Dirac operators are useful in the model of quantum systems with spin, the magnetic fields and relativistic effects. Then, we overview the stability statement of the second kind for quantum complex systems with Coulomb interaction for fermionic matter. After all, it is suggested that mathematical analysis for quantum complex systems is effective in physical problems. |