Observation of Exceptional Points in Electronic Circuits

Two damped coupled oscillators have been used to demonstrate the occurrence of exceptional points in a purely classical system. The implementation was achieved with electronic circuits in the kHz-range. The experimental results perfectly match the mathematical predictions at the exceptional point. A discussion about the universal occurrence of exceptional points -- connecting dissipation with spatial orientation -- concludes the paper.Comment: 4 pages, latex, 3 postscript figures, submitted for publicatio

Chirality of wave functions for three coalescing levels

The coalescence of three levels has particular attractive features. Even though it may be difficult to realise such event in the laboratory (three additional real parameters must be adjusted), to take up the challenge seems worthwhile. In the same way as the chiral behaviour of a usual EP can give a direction on a line, the state vectors in the vicinity of an EP3 provide an orientation in the plane. The distinction between left and right handedness depends on the distribution of the widths of the three levels in the vicinity of the point of coalescence.Comment: Manuscript has been discussed in June 2007 with the experimental group under Professor Achim Richter at the TU Darmstadt. It has been presented at the 6th International Workshop on Pseudo Hermitian Hamiltonians, London, 16-18 July 2007. An expanded version is being prepared for publication. 3 Figures, 11 page

Self-dual Spectral Singularities and Coherent Perfect Absorbing Lasers without PT-symmetry

A PT-symmetric optically active medium that lases at the threshold gain also acts as a complete perfect absorber at the laser wavelength. This is because spectral singularities of PT-symmetric complex potentials are always accompanied by their time-reversal dual. We investigate the significance of PT-symmetry for the appearance of these self-dual spectral singularities. In particular, using a realistic optical system we show that self-dual spectral singularities can emerge also for non-PT-symmetric configurations. This signifies the existence of non-PT-symmetric CPA-lasers.Comment: 11 pages, 3 figures, 1 table, accepted for publication in J. Phys.

Unfolding of eigenvalue surfaces near a diabolic point due to a complex perturbation

The paper presents a new theory of unfolding of eigenvalue surfaces of real symmetric and Hermitian matrices due to an arbitrary complex perturbation near a diabolic point. General asymptotic formulae describing deformations of a conical surface for different kinds of perturbing matrices are derived. As a physical application, singularities of the surfaces of refractive indices in crystal optics are studied.Comment: 23 pages, 7 figure

Application of Pseudo-Hermitian Quantum Mechanics to a Complex Scattering Potential with Point Interactions

We present a generalization of the perturbative construction of the metric operator for non-Hermitian Hamiltonians with more than one perturbation parameter. We use this method to study the non-Hermitian scattering Hamiltonian: H=p^2/2m+\zeta_-\delta(x+a)+\zeta_+\delta(x-a), where \zeta_\pm and a are respectively complex and real parameters and \delta(x) is the Dirac delta function. For regions in the space of coupling constants \zeta_\pm where H is quasi-Hermitian and there are no complex bound states or spectral singularities, we construct a (positive-definite) metric operator \eta and the corresponding equivalent Hermitian Hamiltonian h. \eta turns out to be a (perturbatively) bounded operator for the cases that the imaginary part of the coupling constants have opposite sign, \Im(\zeta_+) = -\Im(\zeta_-). This in particular contains the PT-symmetric case: \zeta_+ = \zeta_-^*. We also calculate the energy expectation values for certain Gaussian wave packets to study the nonlocal nature of \rh or equivalently the non-Hermitian nature of \rH. We show that these physical quantities are not directly sensitive to the presence of PT-symmetry.Comment: 22 pages, 4 figure

Fermionic coherent states for pseudo-Hermitian two-level systems

We introduce creation and annihilation operators of pseudo-Hermitian fermions for two-level systems described by pseudo-Hermitian Hamiltonian with real eigenvalues. This allows the generalization of the fermionic coherent states approach to such systems. Pseudo-fermionic coherent states are constructed as eigenstates of two pseudo-fermion annihilation operators. These coherent states form a bi-normal and bi-overcomplete system, and their evolution governed by the pseudo-Hermitian Hamiltonian is temporally stable. In terms of the introduced pseudo-fermion operators the two-level system' Hamiltonian takes a factorized form similar to that of a harmonic oscillator.Comment: 13 pages (Latex, article class), no figures; v2: some amendments in section 2, seven new refs adde

Characterization of prion disease associated with a two-octapeptide repeat insertion

Genetic prion disease accounts for 10–15% of prion disease. While insertion of four or more octapeptide repeats are clearly pathogenic, smaller repeat insertions have an unclear pathogenicity. The goal of this case series was to provide an insight into the characteristics of the 2-octapeptide repeat genetic variant and to provide insight into the risk for Creutzfeldt–Jakob disease in asymptomatic carriers. 2-octapeptide repeat insertion prion disease cases were collected from the National Prion Disease Pathology Surveillance Center (US), the National Prion Clinic (UK), and the National Creutzfeldt–Jakob Disease Registry (Australia). Three largescale population genetic databases were queried for the 2-octapeptide repeat insertion allele. Eight cases of 2-octapeptide repeat insertion were identified. The cases were indistinguishable from the sporadic Creutzfeldt–Jakob cases of the same molecular subtype. Western blot characterization of the prion protein in the absence of enzymatic digestion with proteinase K revealed that 2-octapeptide repeat insertion and sporadic Creutzfeldt–Jakob disease have distinct prion protein profiles. Interrogation of large-scale population datasets suggested the variant is of very low penetrance. The 2-octapeptide repeat insertion is at most a low-risk genetic variant. Predictive genetic testing for asymptomatic blood relatives is not likely to be justified given the low risk

Spectral Singularities of a General Point Interaction

We study the problem of locating spectral singularities of a general complex point interaction with a support at a single point. We also determine the bound states, examine the special cases where the point interaction is P-, T-, and PT-symmetric, and explore the issue of the coalescence of spectral singularities and bound states.Comment: 11 page

Phylogenomic Discordance Suggests Polytomies Along the Backbone of the Large Genus Solanum

Premise of the study Evolutionary studies require solid phylogenetic frameworks, but increased volumes of phylogenomic data have revealed incongruent topologies among gene trees in many organisms both between and within genomes. Some of these incongruences indicate polytomies that may remain impossible to resolve. Here we investigate the degree of gene-tree discordance in Solanum, one of the largest flowering plant genera that includes the cultivated potato, tomato, and eggplant, as well as 24 minor crop plants. Methods A densely sampled species-level phylogeny of Solanum is built using unpublished and publicly available Sanger sequences comprising 60% of all accepted species (742 spp.) and nine regions (ITS, waxy, and seven plastid markers). The robustness of this topology is tested by examining a full plastome dataset with 140 species and a nuclear target-capture dataset with 39 species of Solanum (Angiosperms353 probe set). Key results While the taxonomic framework of Solanum remained stable, gene tree conflicts and discordance between phylogenetic trees generated from the target-capture and plastome datasets were observed. The latter correspond to regions with short internodal branches, and network analysis and polytomy tests suggest the backbone is composed of three polytomies found at different evolutionary depths. The strongest area of discordance, near the crown node of Solanum, could potentially represent a hard polytomy. Conclusions We argue that incomplete lineage sorting due to rapid diversification is the most likely cause for these polytomies, and that embracing the uncertainty that underlies them is crucial to understand the evolution of large and rapidly radiating lineages

Stochastic pump effect and geometric phases in dissipative and stochastic systems

The success of Berry phases in quantum mechanics stimulated the study of similar phenomena in other areas of physics, including the theory of living cell locomotion and motion of patterns in nonlinear media. More recently, geometric phases have been applied to systems operating in a strongly stochastic environment, such as molecular motors. We discuss such geometric effects in purely classical dissipative stochastic systems and their role in the theory of the stochastic pump effect (SPE).Comment: Review. 35 pages. J. Phys. A: Math, Theor. (in press