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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.
|As Contributors:||Rodrigo Dourado · Miled Moussa|
|Date submitted:||2021-10-11 17:09|
|Submitted by:||Moussa, Miled|
|Submitted to:||SciPost Physics|
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.