Parity-time (PT) symmetry is of great interest. The reciprocal and unidirectional features are intriguing besides the (PT) symmetry phase transition. Recently, the reciprocal transmission, unidirectional reflectionless and invisibility are intensively studied. Here, we show the reciprocal reflection/transmission in (PT)-symmetric system is closely related to the type of (PT) symmetry, that is, ...

We introduce a novel concept of the pseudo-parity-time (pseudo-PT) symmetry in periodically modulated optical systems with balanced gain and loss. We demonstrate that whether or not the original system is PT symmetric, we can manipulate the property of the PT symmetry by applying a periodic modulation in such a way that the effective system derived by the high-frequency Floquet method is PT sym...

The recently proposed complexification of Hamiltonians which keeps the spectra real (and is usually called PT symmetry) is re-interpreted as a certain natural linearalgebraic alternative to Hermiticity. PACS 03.65.Bz, 03.65.Ca 03.65.Fd March 15, 2008, whatis.tex file, J. Phys. A (lett.) Formalism of quantum mechanics is often illustrated by the harmonic oscillator H = p + q. Its eigenstates for...

A fundamental problem in the theory of PT-invariant quantum systems is to determine whether a given system “respects” this symmetry or not. If not, the system usually develops non-real eigenvalues. It is shown in this contribution how to algorithmically detect the existence of complex eigenvalues for a given PT-symmetric matrix. The procedure uses classical results from stability theory which q...

We review quantum mechanical and optical pseudoHermitian systems with an emphasis on PT-symmetric systems important for optics and electrodynamics. One of the most interesting and much discussed consequences of PT symmetry is a phase transition under which the system eigenvalues lose their PT symmetry.We show that although this phase transition is difficult to realize experimentally, a similar ...

In recent years there are new interests on special symmetry in physical systems, called PT-symmetry with various ramifications. Along with the isodual symmetry popularized by RM Santilli, these ideas form one of cornerstone in hadron physics. In the present article, we argue that it is plausible to generalise both ideas to become iso-PT symmetry which indicate there should be new potential obey...

The recently developed notion of parity–time (PT) symmetry in optical systems has spawned intriguing prospects. So far, most experimental implementations have been reported in solid-state systems. Here, we report the first experimental demonstration of optical anti-PT symmetry—the counterpart of conventional PT symmetry—in a warm atomic-vapour cell. Rapid coherence transport via flying atoms le...

The PT-symmetric square well problem is considered in a SUSY framework. When the coupling strength Z lies below the critical value Z (crit) 0 where PT symmetry becomes spontaneously broken, we find a hierarchy of SUSY partner potentials, depicting an unbroken SUSY situation and reducing to the family of sec2-like potentials in the Z → 0 limit. For Z above Z 0 , there is a rich diversity of SUSY...

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 the unitary operator relating an arbitrary non-Hermitian Hamiltonian with exact PT -symmetry to a Hermitian Hamiltonian. We apply our general results to PT symmetry in finite-dimensions and give the explicit form of the...

Developmental dyslexia has been associated with both abnormal hemispheric symmetry of the planum temporale (PT) and a deficit in the magnocellular visual pathway. We examined the relationship between these two abnormalities. Using sagittal magnetic resonance images and three methods, we measured the PT in dyslexic subjects with a documented magnocellular deficit and controls. Dyslexic subjects ...