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arXiv · 2206.15191

Lewis-Riesenfeld invariants for PT-symmetrically coupled oscillators from two dimensional point transformations and Lie algebraic expansions

Andreas Fring·Rebecca Tenney
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Abstract

We construct Lewis-Riesenfeld invariants from two dimensional point transformations for two oscillators that are coupled to each other in space in a PT-symmetrical and time-dependent fashion. The non-Hermitian Hamiltonian of the model is conveniently expressed in terms of generators of the symplectic $sp(4)$ Lie algebra. This allows for an alternative systematic approach to find Lewis-Riesenfeld invariants leading to a set of coupled differential equations that we solve by using time-ordered exponentials. We also demonstrate that point transformations may be utilized to directly construct time-dependent Dyson maps from their respective time-independent counterparts in the reference system.

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Andreas Fring, Rebecca Tenney. 2022-06-30. Lewis-Riesenfeld invariants for PT-symmetrically coupled oscillators from two dimensional point transformations and Lie algebraic expansions. https://doi.org/10.1063/5.0110312

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