TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysCore.5.1.012
TI  - Beyond PT-symmetry: Towards a symmetry-metric relation for time-dependent non-Hermitian Hamiltonians
PY  - 2022/03/14
UR  - https://www.scipost.org/SciPostPhysCore.5.1.012
JF  - SciPost Physics Core
JA  - SciPost Phys. Core
VL  - 5
IS  - 1
SP  - 012
A1  - Alves da Silva, Luís F.
AU  - Dourado, Rodrigo
AU  - Moussa, Miled
AB  - In this work we first propose a method for the derivation of a general continuous antilinear time-dependent (TD) symmetry operator I(t) for a TD non-Hermitian Hamiltonian H(t). Assuming H(t) to be simultaneously ρ(t)-pseudo-Hermitian and Ξ(t)-anti-pseudo-Hermitian, we also derive the antilinear symmetry I(t)=Ξ⁻¹(t)ρ(t), which retrieves an important result obtained by Mostafazadeh [J. Math, Phys. 43, 3944 (2002)] for the time-independent (TI) scenario. We apply our method for the derivaton of the symmetry associated with TD non-Hermitian linear and quadratic Hamiltonians. The computed TD symmetry operators for both cases are then particularized for their equivalent TI lHamiltonians and PT-symmetric restrictions. In the TI scenario we retrieve the well-known Bender-Berry-Mandilara result for the symmetry operator: I^{2k}=1 with k odd [J. Phys. A 35, L467 (2002)]. The results here derived allow us to propose a useful 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 reinforce the prospects of going beyond PT-symmetric quantum mechanics making the field of pseudo-Hermiticity even more comprehensive and promising.
ER  -

@Article{10.21468/SciPostPhysCore.5.1.012,
	title={{Beyond PT-symmetry: Towards a symmetry-metric relation for time-dependent non-Hermitian Hamiltonians}},
	author={Luís F. Alves da Silva and Rodrigo A. Dourado and Miled H. Y. Moussa},
	journal={SciPost Phys. Core},
	volume={5},
	pages={012},
	year={2022},
	publisher={SciPost},
	doi={10.21468/SciPostPhysCore.5.1.012},
	url={https://scipost.org/10.21468/SciPostPhysCore.5.1.012},
}