ar X iv : n uc l - th / 9 70 70 34 v 1 2 1 Ju l 1 99 7 Quantum Transition from Order to Chaos in the Nuclear Shell Model
نویسنده
چکیده
We discuss the role of quantum chaos in atomic nuclei. After reviewing the basic assumptions of the nuclear shell model, we analyze the spectral statistics of the energy levels obtained with realistic shell–model calculations in the f p shell. In particular, for Ca isotopes we observe a transition from order to chaos by increasing the excitation energy and a clear quantum signature of the breaking of integrability by changing the single–particle spacings. Quantum chaos is the study of the properties of quantal systems which are classically chaotic, thus with exponential divergence of initially closed tra-jectories in the phase space [1]. The energy fluctuation properties of systems with underlying classical chaotic behaviour and time–reversal symmetry agree with the predictions of the Gaussian Orthogonal Ensemble (GOE) of random matrix theory, whereas quantum analogs of classically integrable systems display the characteristics of the Poisson statistics [2].
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