TITLE:
Dynamical Phase Transitions in Quantum Systems
AUTHORS:
Ingrid Rotter
KEYWORDS:
Non-Hermitian Quantum Physics, Dynamical Phase Transitions, Phase Rigidity of Eigen-functions, Nonlinear Schrodinger Equation, Exceptional Points
JOURNAL NAME:
Journal of Modern Physics,
Vol.1 No.5,
December
7,
2010
ABSTRACT: Many years ago Bohr characterized the fundamental differences between the two extreme cases of quantum mechanical many-body problems known at that time: between the compound states in nuclei at extremely high level density and the shell-model states in atoms at low level density. It is shown in the present paper that the compound nucleus states at high level density are the result of a dynamical phase transition due to which they have lost any spectroscopic relation to the individual states of the nucleus. The last ones are shell-model states which are of the same type as the shell-model states in atoms. Mathematically, dynamical phase transitions are caused by singular (exceptional) points at which the trajectories of the eigenvalues of the non-Hermitian Hamilton operator cross. In the neighborhood of these singular points, the phases of the eigenfunctions are not rigid. It is possible therefore that some eigenfunctions of the system align to the scattering wavefunctions of the environment by decoupling (trapping) the remaining ones from the environment. In the Schrödinger equation, nonlinear terms appear in the neighborhood of the singular points.