Calculation of Raman Spectra in Quantum Antiferromagnetic Systems containing Spin Gaps

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The quantum effects have a tendency of being hidden in the shadow of classic natures. However, we can find directly quantum effects in antiferromagnetic materials, because the exchange interaction between spins plays an essential role to making quantum natures. Recently, much attention has been paid to "quantum antiferromagnetism" in the low-dimensional systems, for example layer type crystals of Transition-metal oxide compounds. In those systems, ground states are made by singlet dimers. This states have essentially energy gaps, which are called "spin gaps". In order to detect these spin gaps, the experiments of the non-elastic light-scattering process called "magnetic Raman spectrum" are quite influential.This research makes the theoretical calculation for the optical properties originating from magnetic excitations in antiferromagnetic materials. In particular, we make the exact diagonalization in the spin systems for finite numbers. This calculation gives eigenvalues and eigenvectr … More os numerically, which have quite fruitful information in characteristic features of quantum antiferromagnetic systems. In fact, we make the reproduction of Raman spectrum in calculation. Further, spatial correlation functions during spins are obtained numerically. The results suggest us the possibility of new magnetic phases in those systems. Moreover, this research is related closely to Jahn-Teller effect as the problem which concerns the basic mechanism giving the manifestation of the magnetism. Therefore, we examine the relationship between Jahn-Teller effect and the optical spectrum for those quantum antiferromagnetc compounds. In the extension process of the research, we get the viewpoint of the effect caused by "the quantum chaos", which appears in the magnetic g factor. This leads us one of the quite realistic models of "quantum chaos", as well as the new clue to investigations of magnetism. In addition, the developing of the recent experimental research for Bose-condensations in atomic gases gives us the new model which is common to such the quantum-condensed systems. Therefore, we attack actively the problem of Bose-condensations in atomic gases in relation with the process of the occurrence "quantum chaos" in Jahn-Teller effect. Less