Spectral Statistics of a Spin-1/2 Coupled Quartic Oscillators

概要

論文の詳細を見る
The quantum spectral statistical properties, i.e. the nearest neighbor level spacing distribution (NNSD), the mode fluctuation distribution (MFD), the spectral rigidity, etc., of a spin-1/2 particle in three-dimensional coupled quartic oscillator potentials are numerically studied. Changing coupling parameters, the system is continuously transformed from an integrable one to chaotic ones. Various kinds of the Gaussian ensembles (GE's) and the intermediate systems between the integrable class and each GE class can be achieved by selecting non-zero coupling parameters. Especially, this system gives a rare example of the Gaussian symplectic ensemble class. In order to have reliable statistics of quantum levels, it is necessary to evaluate thousands of energy levels from the ground state without missing. We compute the quantum energy levels by numerical diagonalization of the truncated matrix of the Hamiltonian in the basis of harmonic oscillators. Several types of the interpolation formulae of the Poissonian and the Wigner-like distribution of each GE for the NNSD are examined. It is found that the MFD always becomes Gaussian, if the system is chaotic, irrespective of the kinds of the GE's.
理論物理学刊行会の論文
2003-09-30