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Beyond PT-symmetry: Towards a symmetry-metric relation for time-dependent non-Hermitian Hamiltonians. II Parametric amplification

by L. F. Alves da Silva, R. A. Dourado, and M. H. Y. Moussa

This is not the current version.

Submission summary

As Contributors: Rodrigo Dourado · Miled Moussa
Preprint link: scipost_202110_00014v1
Date submitted: 2021-10-11 17:09
Submitted by: Moussa, Miled
Submitted to: SciPost Physics
Academic field: Physics
  • Quantum Physics
Approach: Theoretical


In the present work we apply our method for the derivation of a general continuous antilinear time-dependent (TD) symmetry operator for a TD non-Hermitian quadratic Hamiltonian: a cavity field under parametric amplification. The TD symmetry thus derived is then particularized for the equivalent time-independent (TI) quadratic Hamiltonian and its PT-symmetric restriction. The results here derived together with those for the non-Hermitian linear amplification enables us to propose a symmetry-metric relation for TD non-Hermitian Hamiltonians. From this relation the TD metric is automatically derived from the TD symmetry of the problem. Then, when placed in perspective with the antilinear symmetry I(t)=Ξ⁻¹(t)ρ(t), the symmetry-metric relation finally allow us to derive the Ξ(t)-anti-pseudo-Hermitian operator. Our results reinforces the prospects of going beyond PT-symmetric quantum mechanics making the field of pseudo-Hermitian quantum mechanics even more comprehensive and promissing.

Current status:
Has been resubmitted

Submission & Refereeing History

Resubmission scipost_202110_00014v2 on 1 December 2021

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Submission scipost_202110_00014v1 on 11 October 2021

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