Quantum Dynamics with Non-hermitian Hamiltonians II

Dear Colleagues,

Nowadays, non-Hermitian quantum dynamics is a well-established and continuously growing field of research. Either PT-symmetric or non-PT-symmetric Hamiltonians are usually considered. The symmetric ones represent non-equilibrium systems in a steady state, while the non-PT-symmetric describe systems in more general non-equilibrium states. Because of this, the formulation of the quantum statistical mechanics of general non-Hermitian quantum systems is at least as difficult as the theory of general non-equilibrium statistical systems. Nevertheless, the theoretical applications of non-Hermitian Hamiltonians are found in the fields of condensed matter, optics, and photonics; non-Hermitian Hamiltonians are also used to study exceptional points, resonances, nuclear phenomena, relativistic quantum processes, topological systems, and quantum transport. Let us also not forget that quantum field theory and cosmology are a playground for non-Hermitian mathematical approaches.

However, so far, experimental developments in this field have not been on par with theoretical achievements. Until now, the observation of genuine non-Hermitian dynamics in experiments has only concerned the evolution of classical dissipative systems, theoretically mapped onto quantum-like non-Hermitian dynamics. This can be achieved in a relatively easy manner by means of asymmetric attenuation and amplification. True non-Hermitian evolution of quantum systems is inherently a hard problem since quantum systems naturally follow Hermitian dynamics. Promising ways to achieve a genuine non-Hermitian evolution of quantum systems are given by coupling quantum systems to ancillae and the approach of dilation.

The scope of this Special Issue is broad. The goal is to gather contributions dealing with all the above topics and open problems. The hope is to present the state of the art in non-Hermitian dynamics and to identify the stepping stones for further progress.

Prof. Alessandro Sergi
Prof. Antonino Messina
Guest Editors

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