Spontaneous breaking of classical PT symmetry

Carl M. Bender, Daniel W. Darg
2007 Journal of Mathematical Physics  
The classical trajectories of the family of complex PT-symmetric Hamiltonians H=p^2+x^2(ix)^ϵ (ϵ≥0) form closed orbits. All such complex orbits that have been studied in the past are PT symmetric (left-right symmetric). The periods of these orbits exhibit an unusual dependence on the parameter ϵ. There are regions in ϵ of smooth behavior interspersed with regions of rapid variation. It is demonstrated that the onset of rapid variation is associated with strange new kinds of classical
more » ... s that have never been seen previously. These rare kinds of trajectories are not PT symmetric and occur only for special rational values of ϵ.
doi:10.1063/1.2720279 fatcat:xlwkjsnqbnbmdae5hzlohb7t6a