Unidirectional Invisibility and PT-Symmetry with Graphene

We investigate the reflectionlessness and invisibility properties in the transverse electric (TE) mode solution of a linear homogeneous optical system which comprises the $\mathcal{PT}$-symmetric structures covered by graphene sheets. We derive analytic expressions, indicate roles of each parameter governing optical system with graphene and justify that optimal conditions of these parameters give rise to broadband and wide angle invisibility. Presence of graphene turns out to shift the invisible wavelength range and to reduce the required gain amount considerably, based on its chemical potential and temperature. We substantiate that our results yield broadband reflectionless and invisible configurations for realistic materials of small refractive indices, usually around $\eta = 1$, and of small thickness sizes with graphene sheets of rather small temperatures and chemical potentials. Finally, we demonstrate that pure $\mathcal{PT}$-symmetric graphene yields invisibility at small temperatures and chemical potentials.Comment: 20 pages, 1 table 17 figure

Lax-Phillips scattering theory for PT-symmetric \rho-perturbed operators

The S-matrices corresponding to PT-symmetric \rho-perturbed operators are defined and calculated by means of an approach based on an operator-theoretical interpretation of the Lax-Phillips scattering theory

Quasiprobabilistic Interpretation of Weak measurements in Mesoscopic Junctions

The impossibility of measuring noncommuting quantum mechanical observables is one of the most fascinating consequences of the quantum mechanical postulates. Hence, to date the investigation of quantum measurement and projection is a fundamentally interesting topic. We propose to test the concept of weak measurement of noncommuting observables in mesoscopic transport experiments, using a quasiprobablistic description. We derive an inequality for current correlators, which is satisfied by every classical probability but violated by high-frequency fourth-order cumulants in the quantum regime for experimentally feasible parameters.Comment: 4 pages, published versio

Some properties of eigenvalues and eigenfunctions of the cubic oscillator with imaginary coupling constant

Comparison between the exact value of the spectral zeta function, $Z_{H}(1)=5^{-6/5}[3-2\cos(\pi/5)]\Gamma^2(1/5)/\Gamma(3/5)$, and the results of numeric and WKB calculations supports the conjecture by Bessis that all the eigenvalues of this PT-invariant hamiltonian are real. For one-dimensional Schr\"odinger operators with complex potentials having a monotonic imaginary part, the eigenfunctions (and the imaginary parts of their logarithmic derivatives) have no real zeros.Comment: 6 pages, submitted to J. Phys.

Absence of Normalizable Time-periodic Solutions for The Dirac Equation in Kerr-Newman-dS Black Hole Background

We consider the Dirac equation on the background of a Kerr-Newman-de Sitter black hole. By performing variable separation, we show that there exists no time-periodic and normalizable solution of the Dirac equation. This conclusion holds true even in the extremal case. With respect to previously considered cases, the novelty is represented by the presence, together with a black hole event horizon, of a cosmological (non degenerate) event horizon, which is at the root of the possibility to draw a conclusion on the aforementioned topic in a straightforward way even in the extremal case.Comment: 12 pages. AMS styl

Subnormal operators regarded as generalized observables and compound-system-type normal extension related to su(1,1)

In this paper, subnormal operators, not necessarily bounded, are discussed as generalized observables. In order to describe not only the information about the probability distribution of the output data of their measurement but also a framework of their implementations, we introduce a new concept compound-system-type normal extension, and we derive the compound-system-type normal extension of a subnormal operator, which is defined from an irreducible unitary representation of the algebra su(1,1). The squeezed states are characterized as the eigenvectors of an operator from this viewpoint, and the squeezed states in multi-particle systems are shown to be the eigenvectors of the adjoints of these subnormal operators under a representation. The affine coherent states are discussed in the same context, as well.Comment: LaTeX with iopart.cls, iopart12.clo, iopams.sty, The previous version has some mistake

Spherical functions on the de Sitter group

Matrix elements and spherical functions of irreducible representations of the de Sitter group are studied on the various homogeneous spaces of this group. It is shown that a universal covering of the de Sitter group gives rise to quaternion Euler angles. An explicit form of Casimir and Laplace-Beltrami operators on the homogeneous spaces is given. Different expressions of the matrix elements and spherical functions are given in terms of multiple hypergeometric functions both for finite-dimensional and unitary representations of the principal series of the de Sitter group.Comment: 40 page

Modal Approach to Casimir Forces in Periodic Structures

We present a modal approach to calculate finite temperature Casimir interactions between two periodically modulated surfaces. The scattering formula is used and the reflection matrices of the patterned surfaces are calculated decomposing the electromagnetic field into the natural modes of the structures. The Casimir force gradient from a deeply etched silicon grating is evaluated using the modal approach and compared to experiment for validation. The Casimir force from a two dimensional periodic structure is computed and deviations from the proximity force approximation examined.Comment: 13 pages, 7 figure

Refined algebraic quantisation with the triangular subgroup of SL(2,R)

We investigate refined algebraic quantisation with group averaging in a constrained Hamiltonian system whose gauge group is the connected component of the lower triangular subgroup of SL(2,R). The unreduced phase space is T^*R^{p+q} with p>0 and q>0, and the system has a distinguished classical o(p,q) observable algebra. Group averaging with the geometric average of the right and left invariant measures, invariant under the group inverse, yields a Hilbert space that carries a maximally degenerate principal unitary series representation of O(p,q). The representation is nontrivial iff (p,q) is not (1,1), which is also the condition for the classical reduced phase space to be a symplectic manifold up to a singular subset of measure zero. We present a detailed comparison to an algebraic quantisation that imposes the constraints in the sense H_a Psi = 0 and postulates self-adjointness of the o(p,q) observables. Under certain technical assumptions that parallel those of the group averaging theory, this algebraic quantisation gives no quantum theory when (p,q) = (1,2) or (2,1), or when p>1, q>1 and p+q is odd.Comment: 30 pages. LaTeX with amsfonts, amsmath, amssymb. (v4: Typos corrected. Published version.

q-Deformed de Sitter/Conformal Field Theory Correspondence

Unitary principal series representations of the conformal group appear in the dS/CFT correspondence. These are infinite dimensional irreducible representations, without highest weights. In earlier work of Guijosa and the author it was shown for the case of two-dimensional de Sitter, there was a natural q-deformation of the conformal group, with q a root of unity, where the unitary principal series representations become finite-dimensional cyclic unitary representations. Formulating a version of the dS/CFT correspondence using these representations can lead to a description with a finite-dimensional Hilbert space and unitary evolution. In the present work, we generalize to the case of quantum-deformed three-dimensional de Sitter spacetime and compute the entanglement entropy of a quantum field across the cosmological horizon.Comment: 18 pages, 2 figures, revtex, (v2 reference added