Non-Hermitian time evolution: From static to parametric instability

  title={Non-Hermitian time evolution: From static to parametric instability},
  author={Aleksi Bossart and Romain Fleury},
  journal={Physical Review A},
Eigenmode coalescence imparts remarkable properties to non-hermitian time evolution, culminating in a purely non-hermitian spectral degeneracy known as an exceptional point (EP). Here, we revisit time evolution at the EP and classify two-level non-hermitian Hamiltonians in terms of the Möbius group. We then leverage that classification to study dynamical EP encircling, by applying it to periodically-modulated (Floquet) Hamiltonians. This reveals that Floquet non-hermitian systems exhibit rich… 
1 Citations

Figures from this paper

Photonics of time-varying media

Abstract. Time-varying media have recently emerged as a new paradigm for wave manipulation, due to the synergy between the discovery of highly nonlinear materials, such as epsilon-near-zero



IEEE Transactions on Antennas and Propagation

  • Business
    IEEE Transactions on Antennas and Propagation
  • 2021

Prospects and fundamental limits in exceptional point-based sensing

Exotic degeneracies in open quantum systems, so-called exceptional points, show rich physics and promise new applications, such as sensors with greatly enhanced response, as well as limits of such sensors due to excess quantum noise.

Revealing the missing dimension at an exceptional point

The radiation of electromagnetic and mechanical waves depends not only on the intrinsic properties of the emitter but also on the surrounding environment. This principle has laid the foundation for

Sensitive readout of implantable microsensors using a wireless system locked to an exceptional point

It is shown that a reconfigurable wireless system locked to an exceptional point can be used to interrogate in vivo microsensors with a sensitivity 3.2 times beyond the limit of conventional readout schemes.

Exact Floquet solutions in a periodically driven non-Hermitian parity-time symmetric two-level model

We investigate a type of periodically driven non-Hermitian two-level model with parity-time (PT) symmetry. It is shown that in a wide range of the model parameters, this model supports exact Floquet

Annales scientifiques de ľÉcole Normale Supérieure

  • 1891

Journal de Mathématiques pures et appliquées

  • 1889

On the observability and asymmetry of adiabatic state flips generated by exceptional points

In open quantum systems where the effective Hamiltonian is not Hermitian, it is known that the adiabatic (or instantaneous) basis can be multivalued: by adiabatically transporting an eigenstate along

Perturbation theory for linear operators