Real energies and Berry phases in all PT-regimes in time-dependent non-Hermitian theories

Abstract

We demonstrate that the existence of a Hermitian time-dependent intertwining operator that maps the non-Hermitian time-dependent energy operator to its Hermitian conjugate and its right to its left eigenstates guarantees the reality of the instantaneous energies. This property holds throughout all three $\mathcal{P}\mathcal{T}$-regimes, in the time-independent scenario referred to as the $\mathcal{P}\mathcal{T}$-symmetric regime, the exceptional point and the spontaneously broken $\mathcal{P}\mathcal{T}$-regime. We also propose a modified adiabatic approximation consisting of an expansion of the wavefunctions in terms the instantaneous eigenstates of the energy operator, instead of the usually used eigenfunctions of the Hamiltonian. We show that this proposal always leads to real Berry phases. We illustrate the working of our general proposals with two explicit examples for a time-dependent non-Hermitian spin model.

12 pages

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Cited by in corpus (5)

• Discrete-coordinate crypto-Hermitian quantum system controlled by time-dependent Robin boundary conditions
• Quasi-Hermitian formulation of quantum mechanics using two conjugate Schrödinger equations
• PT-symmetric dynamical confinement: Fermi acceleration, quantum force and Berry phase
• Three alternative model-building strategies using quasi-Hermitian time-dependent observables
• Emergence and localization of exceptional points in an exactly solvable toy model