Quantum chaos and dynamical systems

Methods of Modern Mathematical Physics

Random-matrix physics: spectrum and strength fluctuations

It now appears that the general nature of the deviations from uniformity in the spectrum of a complicated nucleus is essentially the same in all regions of the spectrum and over the entire Periodic Table. This behavior, moreover, is describable in terms of standard Hamiltonian ensembles which could be generated on the basis of simple information-theory concepts, and which give also a good account of fluctuation phenomena of other kinds and, apparently, in other many-body systems besides nuclei. The main departures from simple behavior are ascribable to the moderation of the level repulsion by effects due to symmetries and collectivities, for the description of which more complicated ensembles are called for. One purpose of this review is to give a self-contained account of the theory, using methods---sometimes approximate---which are consonant with the usual theory of stochastic processes. Another purpose is to give a proper foundation for the use of ensemble theory, to make clear the origin of the simplicities in the observable fluctuations, and to derive other general fluctuation results. In comparing theory and experiment, the authors give an analysis of much of the nuclear-energy-level data, as well as an extended discussion of observable effects in nuclear transitions and reactions and in the low-temperature thermodynamics of aggregates of small metallic particles.

Geometric Phases in Physics

During the last few years, considerable interest has been focused on the phase that waves accumulate when the equations governing the waves vary slowly. The recent flurry of activity was set off by a paper by Michael Berry, where it was found that the adiabatic evolution of energy eigenfunctions in quantum mechanics contains a phase of geometric origin (now known as 'Berry's phase') in addition to the usual dynamical phase derived from Schrödinger's equation. This observation, though basically elementary, seems to be quite profound. Phases with similar mathematical origins have been identified

Relation between the Quadrupole Moments and the Widths of the Giant Resonance of Photonuclear Reaction

Progress of Theoretical Physics Vol. 16 No. 2 (1956) pp. 112–130 On Quantum-Mechanical Nuclear Dipole Vibrations Jun-ichi Fujita

On the Excited States of Even-even Nuclei

Progress of Theoretical Physics Vol. 15 No. 4 (1956) pp. 416–417:Note on the Nuclear Level of SPin 2+ Mitsuo Sakai Progress of Theoretical Physics Vol. 15 No. 5 (1956) pp. 445–460:Proposal for Experiments for Determination of Beta-Decay Interaction and Theory of Triple Cascade Transition Masato Morita