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arXiv · 1610.09273

On the invariant method for the time-dependent non-Hermitian Hamiltonians

Boubakeur Khantoul·A. Bounames·M. Maamache
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Abstract

We propose a scheme to deal with certain time-dependent non-Hermitian Hamiltonian operators $H(t)$ that generate a real phase in their time-evolution. This involves the use of invariant operators $I_{PH}(t)$ that are pseudo-Hermitian with respect to the time-dependent metric operator, which implies that the dynamics is governed by unitary time evolution. Furthermore, $H(t)$ is not generally quasi-Hermitian and does not define an observable of the system but $I_{PH}(t)$ obeys a quasi-hermiticity transformation as in the completely time-independent Hamiltonian systems case. The harmonic oscillator with a time-dependent frequency under the action of a complex time-dependent linear potential is considered as an illustrative example.

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Boubakeur Khantoul, A. Bounames, M. Maamache. 2016-10-28. On the invariant method for the time-dependent non-Hermitian Hamiltonians. https://doi.org/10.1140/epjp/i2017-11524-7

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