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)

References in corpus (3)

• Making Sense of Non-Hermitian Hamiltonians
• Mixed-state evolution in the presence of gain and loss
• An example of interplay between Physics and Mathematics: Exact resolution of a new class of Riccati Equations

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