Hermitian dynamics in a class of pseudo-Hermitian networks

Jin, L.; Song, Z.

doi:10.48550/arxiv.1107.4311

Cited by 1 publication

(2 citation statements)

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“…From Eq. (61) we see that E F = E B ≡ E. The isometry can be read off from relation (48) for the eigenvector φ ± and φ ′ ± ,…”

Section: Physical Realization In the Rabi Problem A Preliminary Resultsmentioning

confidence: 94%

“…A second-quantization approach of the semiclassical damped Rabi problem proposed in the present work can be investigated following a treatment in the same lines as the one presented in [47]. Finally, the developed formalism might be extendable to lattice systems [48], and in this case topological phase transitions in the exceptional points could be investigated, as done for optical lattices [49].…”

Section: Final Remarksmentioning

confidence: 91%

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Classical-quantum correspondence for two-level pseudo-Hermitian systems

Raimundo,

Baldiotti,

Fresneda

et al. 2020

Preprint

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In this work, a classical/quantum correspondence for a pseudo-hermitian system with finite energy levels is proposed and analyzed. We show that the presence of a complex external field can be described by a pseudo-hermitian Hamiltonian if there is a suitable canonical transformation that links it to a real field. We construct a covariant quantization scheme which maps canonically related pseudoclassical theories to unitarily equivalent quantum realizations, such that there is a unique metric-inducing isometry between the distinct Hilbert spaces. In this setting, the pseudo-hermiticity condition for the operators induces an involution which guarantees the reality of the corresponding symbols, even for the complex field case. We assign a physical meaning for the dynamics in the presence of a complex field by constructing a classical correspondence. As an application of our theoretical framework, we propose a damped version of the Rabi problem and determine the configuration of the parameters of the setup for which damping is completely suppressed.

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“…From Eq. (61) we see that E F = E B ≡ E. The isometry can be read off from relation (48) for the eigenvector φ ± and φ ′ ± ,…”

Section: Physical Realization In the Rabi Problem A Preliminary Resultsmentioning

confidence: 94%