Non-Hermitian theory is a theoretical framework used to describe open systems. It offers a
powerful tool in the characterization of both the intrinsic degrees of freedom of a system and …

It is generally assumed that a Hamiltonian for a physically acceptable quantum system (one
that has a positive-definite spectrum and obeys the requirement of unitarity) must be …

This chapter introduces the basic ideas of P T-symmetric systems. It begins with a brief
discussion of closed (isolated) and open (non-isolated) systems and explains that P T …

The Hamiltonian H specifies the energy levels and time evolution of a quantum theory. A
standard axiom of quantum mechanics requires that H be Hermitian because Hermiticity …

We review quantum mechanical and optical pseudo-Hermitian systems with an emphasis on
PT-symmetric systems important for optics and electrodynamics. One of the most interesting …

We study entanglement properties of free-fermion systems without Hermiticity by use of
correlation matrix and overlap matrix in the biorthogonal basis. We find at a critical point in …

The basic properties of Floquet-Bloch (FB) modes in parity-time (PT)-symmetric optical
lattices are examined in detail. Due to the parity-time symmetry of such complex periodic …

Bound state in a continuum (BIC) is a spatially confined resonance with its energy
embedded in a continuous spectrum of propagative modes, yet their coupling is prohibited …

Abstract For a non-Hermitian Hamiltonian H possessing a real spectrum, we introduce a
canonical orthonormal basis in which a previously introduced unitary mapping of H to a …

We consider the ratchet dynamics in a PT-symmetric Floquet quantum system with
symmetric temporal (harmonic) driving. In the exact PT-symmetry phase, for a finite number …