Analytically solvable $2\times 2$ $PT$-symmetry dynamics from su(1,1)-symmetry problems

Abstract

A protocol for explicitly constructing the exact time-evolution operators generated by $2\times 2$ time-dependent $PT$-symmetry Hamiltonians is reported. Its mathematical applicability is illustrated with the help of appropriate examples. The physical relevance of the proposed approach within gain-loss system scenarios, like two-coupled wave-guides, is discussed in detail.

7 pages and 3 figures (5 plots)