Riccardo Giachetti, Vincenzo Grecchi
We make a nodal analysis of the processes of level crossings in a model of quantum mechanics with a PT-symmetric double well. We prove the existence of infinite crossings with their selection rules. At the crossing, before the PT-symmetry breaking and the localization, we have a total P-symmetry breaking of the states.
http://arxiv.org/abs/1410.8460
Mathematical Physics (math-ph)
S. Bittner, B. Dietz, U. Guenther, H. L. Harney, M. Miski-Oglu, A. Richter, F. Schaefer
We demonstrate the presence of parity-time (PT) symmetry for the non-Hermitian two-state Hamiltonian of a dissipative microwave billiard in the vicinity of an exceptional point (EP). The shape of the billiard depends on two parameters. The Hamiltonian is determined from the measured resonance spectrum on a fine grid in the parameter plane. On a curve, which passes through the EP, the Hamiltonian has either real or complex conjugate eigenvalues. An appropriate basis choice reveals its PT symmetry. Spontaneous symmetry breaking occurs at the EP.
http://arxiv.org/abs/1107.4256
Quantum Physics (quant-ph); Mathematical Physics (math-ph)