Related papers: A reality proof in PT-symmetric quantum mechanics
Recent experimental tests of the symmetrization postulate of quantum mechanics are discussed. It is shown that in a strict sense these experiments cannot test the validity of the symmetrization postulate, but in most cases do test the…
Canonical quantum mechanics postulates Hermitian Hamiltonians to ensure real eigenvalues. Counterintuitively, a non-Hermitian Hamiltonian, satisfying combined parity-time (PT) symmetry, could display entirely real spectra above some…
The purpose of this paper is the discussion of a pair of coupled linear oscillators that has recently been proposed as a model of a system of two optical resonators. By means of an algebraic approach we show that the frequencies of the…
Parity-time ($PT$) symmetric Hamiltonians are generally non-Hermitian and give rise to exotic behaviour in quantum systems at exceptional points, where eigenvectors coalesce. The recent realisation of $PT$-symmetric Hamiltonians in quantum…
Two alternative scenarios are shown possible in Quantum Mechanics working with non-Hermitian $PT-$symmetric form of observables. While, usually, people assume that $P$ is a self-adjoint indefinite metric in Hilbert space (and that their…
We investigate the scattering response of parity-time (PT) symmetric structures. We show that, due to the local flow of energy between gain and loss regions, such systems can deflect light in unusual ways, as a function of the gain/loss…
We survey some of the main conceptual developments in the study of PT-symmetric and pseudo-Hermitian Hamiltonian operators that have taken place during the past ten years or so. We offer a precise mathematical description of a quantum…
The aim of this paper is to give a simple, geometric proof of Wigner's theorem on the realization of symmetries in quantum mechanics that clarifies its relation to projective geometry. Although several proofs exist already, it seems that…
We demonstrate that a coherently-prepared four-level atomic medium can provide a versatile platform for realizing parity-time (PT) symmetric optical potentials. Different types of PT-symmetric potentials are proposed by appropriately tuning…
Non-Hermitian systems based on parity-time (PT) symmetry reveal rich physics beyond the Hermitian regime. So far, realizations of PT-symmetric systems have been limited to the spatial domain. Here we theoretically and experimentally…
We show that any unitary transformation performed on the quantum state of a closed quantum system, describes an inner, reversible, generalized quantum measurement. We also show that under some specific conditions it is possible to perform a…
The implications of the physical theory of quantum mechanics on the question of realism is much a subject of sustaining interest, while the background questions among physicists on how to think about all the theoretical notion and…
Spectral singularities are certain points of the continuous spectrum of generic complex scattering potentials. We review the recent developments leading to the discovery of their physical meaning, consequences, and generalizations. In…
The recently theoretical and experimental researches related to $\mathcal{PT}$-symmetric system have attracted unprecedented attention because of various novel features and potentials in extending canonical quantum mechanics. However, as…
We consider symmetry as a foundational concept in quantum mechanics and rewrite quantum mechanics and measurement axioms in this description. We argue that issues related to measurements and physical reality of states can be better…
For a general complex scattering potential defined on a real line, we show that the equations governing invisibility of the potential are invariant under the combined action of parity and time-reversal (PT) transformation. We determine the…
Through a new interpretation of Special Theory of Relativity and with a model given for physical space, we can find a way to understand the basic principles of Quantum Mechanics consistently from Classical Theory. It is supposed that…
The mathematical model of orthodox quantum mechanics has been critically examined and some deficiencies have been summarized. The model based on the extended Hilbert space and free of these shortages has been proposed; parameters being…
A real band condition is shown to exist for one dimensional periodic complex non-hermitian potentials exhibiting PT-symmetry. We use an exactly solvable ultralocal periodic potential to obtain the band structure and discuss some spectral…
This paper describes an algorithmic system called SQT for the computer simulation of a wide class of quantum experiments on entangled particles. SQT maintains a hidden internal state for each particle and it provides an initialization…