Distant perturbation asymptotics in window-coupled waveguides. I. The non-threshold case

We consider a pair of adjacent quantum waveguides, in general of different widths, coupled laterally by a pair of windows in the common boundary, not necessarily of the same length, at a fixed distance. The Hamiltonian is the respective Dirichlet Laplacian. We analyze the asymptotic behavior of the discrete spectrum as the window distance tends to infinity for the generic case, i.e. for eigenvalues of the corresponding one-window problems separated from the threshold

Time dependent partial waves and vortex rings in the dynamics of wave packets

We have found a new class of time dependent partial waves which are solutions of time dependent Schr\"odinger equation for three dimensional harmonic oscillator. We also showed the decomposition of coherent states of harmonic oscillator into these partial waves. This decomposition appears perticularly convenient for a description of the dynamics of a wave packet representing a particle with spin when the spin--orbit interaction is present in the hamiltonian. An example of an evolution of a localized wave packet into a torus and backwards, for a particular initial conditions is analysed in analytical terms and shown with a computer graphics.Comment: 10 pages, LaTeX, 6 postscript figures, submitted to J. Phys. A: Math. Ge

PT-symmetric models in curved manifolds

We consider the Laplace-Beltrami operator in tubular neighbourhoods of curves on two-dimensional Riemannian manifolds, subject to non-Hermitian parity and time preserving boundary conditions. We are interested in the interplay between the geometry and spectrum. After introducing a suitable Hilbert space framework in the general situation, which enables us to realize the Laplace-Beltrami operator as an m-sectorial operator, we focus on solvable models defined on manifolds of constant curvature. In some situations, notably for non-Hermitian Robin-type boundary conditions, we are able to prove either the reality of the spectrum or the existence of complex conjugate pairs of eigenvalues, and establish similarity of the non-Hermitian m-sectorial operators to normal or self-adjoint operators. The study is illustrated by numerical computations.Comment: 37 pages, PDFLaTeX with 11 figure

On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators

We consider one-dimensional Schroedinger-type operators in a bounded interval with non-self-adjoint Robin-type boundary conditions. It is well known that such operators are generically conjugate to normal operators via a similarity transformation. Motivated by recent interests in quasi-Hermitian Hamiltonians in quantum mechanics, we study properties of the transformations in detail. We show that they can be expressed as the sum of the identity and an integral Hilbert-Schmidt operator. In the case of parity and time reversal boundary conditions, we establish closed integral-type formulae for the similarity transformations, derive the similar self-adjoint operator and also find the associated "charge conjugation" operator, which plays the role of fundamental symmetry in a Krein-space reformulation of the problem.Comment: 27 page

Generic Wrappers

Component software means reuse and separate marketing of pre-manufactured binary components. This requires components from different vendors to be composed very late, possibly by end users at run time as in compound-document frameworks. To this aim, we propose generic wrappers, a new language construct for stronglytyped class-based languages. With generic wrappers, objects can be aggregated at run time. The aggregate belongs to a subtype of the actual type of the wrapped object. A lower bound for the type of the wrapped object is fixed at compile time. Generic wrappers are type safe and support modular reasoning. This feature combination is required for true component software but not achieved by known wrapping and combination techniques, such as the wrapper pattern or mix-ins. We analyze the design space for generic wrappers, e.g. overriding, forwarding vs. delegation, and snappy binding of the wrapped object. As a proof of concept, we add generic wrappers to Java and report on a mechanized type soundness proof of the latter