On the invariant method for the time-dependent non-Hermitian Hamiltonians
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 impl...
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| creator | Khantoul, Boubakeur Bounames, A Maamache, M |
| description | 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. |
| doi_str_mv | 10.48550/arxiv.1610.09273 |
| format | Article |
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| subjects | Evolution Hamiltonian functions Harmonic oscillators Invariants Operators Physics - Quantum Physics Time dependence |
| title | On the invariant method for the time-dependent non-Hermitian Hamiltonians |
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