Both theoretical and experimental studies of topological phases in non-Hermitian systems
have made a remarkable progress in the last few years of research. In this article, we review …

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 …

Requiring that a Hamiltonian be Hermitian is overly restrictive. A consistent physical theory
of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but …

The nonlinear supersymmetric (SUSY) approach to spectral problems in quantum
mechanics (QM) is reviewed. Its building from the chains (ladders) of linear SUSY systems is …

A diagonalizable non-Hermitian Hamiltonian having a real spectrum may be used to define
a unitary quantum system, if one modifies the inner product of the Hilbert space properly. We …

A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian
that is not Hermitian but instead satisfies the physical condition of space–time reflection …

We show that a quantum system possessing an exact antilinear symmetry, in particular PT-
symmetry, is equivalent to a quantum system having a Hermitian Hamiltonian. We construct …

We systematically study a Kitaev chain with imbalanced pair creation and annihilation,
which is introduced by non-Hermitian pairing terms. An exact phase diagram shows that the …

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