2016/10/12 by Lawrence R. Mead, David Garfinkle, Mead, Lawrence R. +1
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Physics (quant-ph) #hep-th #quant-ph
paper · pdf · doi:10.48550/arxiv.1610.03801
13 pages, 2 figures
arxiv created 2016/10/12 · arxiv updated 2016/10/13
Carl Bender and collaborators have developed a quantum theory governed by Hamiltonians that are PT-symmetric rather than Hermitian. To implement this theory, the inner product was redefined to guarantee positive norms of eigenstates of the Hamiltonian. In the general case, which includes arbitrary time-dependence in the Hamiltonian, a modification of the Schrodinger equation is necessary as shown by Gong and Wang to conserve probability. In this paper, we derive the following selection rule: transitions induced by time dependence in a PT-symmetric Hamiltonian cannot occur between normalized states of differing PT-norm. We show three examples of this selection rule in action: two matrix models and one in the continuum.