Currently, it has been claimed that certain Hermitian Hamiltonians have parity (P) and they are PT-invariant. We propose generalized definitions of time-reversal operator (T) and orthonormality such that all Hermitian Hamil-tonians are P, T, PT, and CPT invariant. The PT-norm and CPT-norm are indefinite and definite respectively. The energy-eigenstates are either E-type (e.g., even) or O-type (...

Synthetic non-conservative systems with parity-time (PT) symmetric gain-loss structures can exhibit unusual spontaneous symmetry breaking that accompanies spectral singularity. Recent studies on PT symmetry in optics and weakly interacting open quantum systems have revealed intriguing physical properties, yet many-body correlations still play no role. Here by extending the idea of PT symmetry t...

Parity-time (PT) symmetric structures present the unidirectional invisibility at the spontaneous PT-symmetry breaking point. In this paper, we propose a PT-symmetric circuit consisting of a resistor and a microwave tunnel diode (TD) which represent the attenuation and amplification, respectively. Based on the scattering matrix method, the circuit can exhibit an ideal unidirectional performance ...

Symmetry breaking of solitons in a class of one-dimensional parity-time (PT) symmetric complex potentials with cubic nonlinearity is reported. In generic PT-symmetric potentials, such symmetry breaking is forbidden. However, in a special class of PT-symmetric potentials V(x)=g(2)(x)+αg(x)+ig'(x), where g(x) is a real and even function and α a real constant, symmetry breaking of solitons can occ...

The concept of parity-time (PT) symmetry in SPPs is proposed and confirmed for the first time in this work. By introducing periodic modulation of the effective refractive index in SPP system, the asymmetric propagation is theoretically predicted and numerically demonstrated. After validation of this concept, we apply it in two applications: PT-waveguide and PT-cloak. Both two applications furth...

We study the effect of nonlinearity on systems with periodic parity-time (PT) symmetry, and show that nonlinearity can transform the system from broken to full PT symmetry and vice versa. Furthermore, we show that even when the nonlinearity is insufficient to induce a transition from broken to full PT symmetry, still, the wave functions neither decay nor diverge, despite the fact that the syste...

Motivated by the duality of normalizable states and the presence of the quasi-parity quantum number q = ±1 in PT symmetric (non-Hermitian) quantum mechanical potential models, the relation of PT symmetry and supersymmetry (SUSY) is studied. As an illustrative example the PT invariant version of the Scarf II potential is presented, and it is shown that the “bosonic” Hamiltonian has two different...

Multidimensional complex optical potentials with partial parity-time (PT) symmetry are proposed. The usual PT symmetry requires that the potential is invariant under complex conjugation and simultaneous reflection in all spatial directions. However, we show that if the potential is only partially PT symmetric, i.e., it is invariant under complex conjugation and reflection in a single spatial di...

We discuss phase transitions in PT -symmetric optical systems. We show that, due to frequency dispersion of the dielectric permittivity, an optical system can have PT symmetry at isolated frequency points only. An assumption of the existence of a PT -symmetric system in a continuous frequency interval violates the causality principle. Therefore, the ideal symmetry-breaking transition cannot be ...

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 satisfies the less restrictive and more physical condition of space-time reflection symmetry (PT symmetry). One might expect a non-Hermitian Hamiltonian to lead to a violation of unitarity. However, if PT symmetry is n...