While Hermiticity of a time-independent Hamiltonian leads to unitary time evolution, in and of itself, the requirement of Hermiticity is only sufficient for unitary time evolution. In this paper, we provide conditions that are both necessary and sufficient. We show that PT symmetry of a time-independent Hamiltonian, or equivalently, reality of the secular equation that determines its eigenvalue...

Abstract Non-Hermitian Hamiltonians, which effectively describe dissipative systems, and analogue gravity models, simulate properties of gravitational objects, comprise seemingly different areas current research. Here, we investigate the interplay between two by relating parity-time-symmetric Weyl-type Hamiltonians to Schwarzschild black holes emitting Hawking radiation. We show that exceptiona...

The appearances of complex eigenvalues in the spectra of PT -symmetric quantummechanical systems are usually associated with a spontaneous breaking of PT . In this letter we discuss a family of models for which this phenomenon is also linked with an explicit breaking of supersymmetry. Exact level-crossings are located, and connections with N -fold supersymmetry and quasi-exact solvability in ce...

A generalization of the concept of PT −symmetric Hamiltonians H = p + V (x) is presented. For the usual analytic potentials V (x) (with singularities) and for the recently widely accepted “PT −symmetric” asymptotic boundary conditions for wave functions ψ(x) (selected inside a pair of complex wedges generalizing the usual x → ±∞ asymptotics), non-equivalent quantum toboggans are defined as inte...

The main achievements of Pseudo-Hermitian Quantum Mechanics and its distinction with the indefinite-metric quantum theories are reviewed. The issue of the non-uniqueness of the metric operator and its consequences for defining the observables are discussed. A systematic perturbative expression for the most general metric operator is offered and its application for a toy model is outlined.