Pseudo PT -symmetry in time periodic non-Hermitian Hamiltonians systems

Abstract

We investigate the concept of the pseudo-parity–time (pseudo-PT) symmetry in periodic quantum systems. This pseudo par-ity–time symmetry manifests it self dynamically in the framework of the non-unitary evolution(Floquet)operator U(τ)=e−iLτ,overa eriodτ, which shows that the stability of the dynamics occurs when the PT-ymmetry(orpseudo-PT)ofthetime-independentnon-Hermitian Hamiltonian L is unbroken i.e. its quasienergies En are real. Nevertheless, when the PT-symmetry of the non-Hermitian Hamiltonian L is broken,which corresponds to the com-plex conjugate quasienergies En, an instable dynamics arises. We investigate in greater detail a harmonic oscillator with maginary time-dependent periodic driving term linear in x.TheFloquetop-erator for the modulated system is pseudo-PT symmetric if the relative phase φ of the applied mode is not 0 or π.