Dynamical phase transitions in quantum mechanics

Abstract

The nucleus is described as an open many-body quantum system with a non- Hermitian Hamilton operator the eigenvalues of which are complex, in general. The eigen- values may cross in the complex plane (exceptional points), the phases of the eigenfunc- tions are not rigid in approaching the crossing points and the widths bifurcate. By varying only one parameter, the eigenvalue trajectories usually avoid crossing and width bifurca- tion occurs at the critical value of avoided crossing. An analog spectroscopic redistribution takes place for discrete states below the particle decay threshold. By this means, a dynam- ical phase transition occurs in the many-level system starting at a critical value of the level density. Hence the properties of the low-lying nuclear states (described well by the shell model) and those of highly excited nuclear states (described by random ensembles) di er fundamentally from one another. The statement of Niels Bohr on the collective features of compound nucleus states at high level density is therefore not in contradiction to the shell-model description of nuclear (and atomic) states at low level density. Dynamical phase transitions are observed experimentally in di erent quantum mechanical systems by varying one or two parameters.