Piecewise Adiabatic Following in Non-Hermitian Cycling

Abstract

The time evolution of periodically driven non-Hermitian systems is in general non-unitary but can be stable. It is hence of considerable interest to examine the adiabatic following dynamics in periodically driven non-Hermitian systems. We show in this work the possibility of piecewise adiabatic following interrupted by hopping between instantaneous system eigenstates. This phenomenon is first observed in a computational model and then theoretically explained, using an exactly solvable model, in terms of the Stokes phenomenon. In the latter case, the piecewise adiabatic following is shown to be a genuine critical behavior and the precise phase boundary in the parameter space is located. Interestingly, the critical boundary for piecewise adiabatic following is found to be unrelated to the domain for exceptional points. To characterize the adiabatic following dynamics, we also advocate a simple definition of the Aharonov-Anandan (AA) phase for non-unitary cyclic dynamics, which always yields real AA phases. In the slow driving limit, the AA phase reduces to the Berry phase if adiabatic following persists throughout the driving without hopping, but oscillates violently and does not approach any limit in cases of piecewise adiabatic following. This work exposes the rich features of non-unitary dynamics in cases of slow cycling and should stimulate future applications of non-unitary dynamics.

10 pages, 7 figures

References in corpus (13)

• Making Sense of Non-Hermitian Hamiltonians
• Dynamically encircling exceptional points in a waveguide: asymmetric mode switching from the breakdown of adiabaticity
• Loss-induced suppression and revival of lasing
• PT-symmetry breaking and laser-absorber modes in optical scattering systems
• Spawning rings of exceptional points out of Dirac cones
• PT-Symmetric Phonon Laser
• Reversing the Pump-Dependence of a Laser at an Exceptional Point
• A review of progress in the physics of open quantum systems: theory and experiment
• PT-Symmetric Wave Chaos
• Chiral state-conversion without encircling an exceptional point
• PT spectroscopy of the Rabi problem
• Stabilizing Non-Hermitian Systems by Periodic Driving
• PT-symmetric Rabi model: Perturbation theory

Cited by in corpus (11)

• Dynamical quantum phase transitions in non-Hermitian lattices
• Non-Hermitian Floquet topological phases with arbitrarily many real-quasienergy edge states
• Dual topological characterization of non-Hermitian Floquet phases
• Anomaly in dynamical quantum phase transition in non-Hermitian system with extended gapless phases
• Non-Hermitian dynamics of slowly-varying Hamiltonians
• Complex Berry phase and imperfect non-Hermitian phase transitions
• Pseudo-invariant approach for a particle in a complex time-dependent linear potential
• Piecewise Adiabatic Following: General Analysis and Exactly Solvable Models
• Persistent anomaly in dynamical quantum phase transition in long-range non-Hermitian $p$-wave Kitaev chain
• Classical correspondence of the exceptional points in the finite non-Hermitian system
• Non-adiabatic transitions in parabolic and super-parabolic $\mathcal{P}\mathcal{T}$-symmetric non-Hermitian systems