Weyl formulas for annular ray-splitting billiards

We consider the distribution of eigenvalues for the wave equation in annular (electromagnetic or acoustic) ray-splitting billiards. These systems are interesting in that the derivation of the associated smoothed spectral counting function can be considered as a canonical problem. This is achieved by extending a formalism developed by Berry and Howls for ordinary (without ray-splitting) billiards. Our results are confirmed by numerical computations and permit us to infer a set of rules useful in order to obtain Weyl formulas for more general ray-splitting billiards

In-vitro resistance of cloned human glioma cells to natural killer activity of allogeneic peripheral lymphocytes.

Cells from an established culture of a human astrocytoma were incubated with normal allogeneic peripheral lymphocytes (PBL) in order to study the natural killer (NK) sensitivity of the in vitro propagated cell line. A proportion of cells in culture formed halos, into which lymphocytes did not penetrate. These cells were successfully cloned and showed a decreased susceptibility to NK cytolysis compared with the parent line. Both cell lines could be transplanted into athymic nude mice. The cloned NK-resistant cells underwent a frequent spontaneous regression in nu/nu mice, despite the fact that when used as targets for nu/nu NK cells in vitro they were only moderately susceptible. Phase-contrast microscopy of the mass-cultured cells co-cultivated with lymphocytes suggested that their morphology and ability to form inpenetrable translucent halos might influence their susceptibility to NK lysis. Experiments performed on this assumption revealed that quiescent and halo forming tumour cells were not the primary targets for NK lysis. Cells in mass culture, although tumorigenic, were thus heterogeneous in respect of susceptibility to NK attack. These findings might be relevant to the mechanism of immune escape and tumour heterogeneity in respect of spontaneous cell-mediated lysis

One-dimensional quantum chaos: Explicitly solvable cases

We present quantum graphs with remarkably regular spectral characteristics. We call them {\it regular quantum graphs}. Although regular quantum graphs are strongly chaotic in the classical limit, their quantum spectra are explicitly solvable in terms of periodic orbits. We present analytical solutions for the spectrum of regular quantum graphs in the form of explicit and exact periodic orbit expansions for each individual energy level.Comment: 9 pages and 4 figure

Diagnostic criterion for crystallized beams

Small ion crystals in a Paul trap are stable even in the absence of laser cooling. Based on this theoretically and experimentally well-established fact we propose the following diagnostic criterion for establishing the presence of a crystallized beam: Absence of heating following the shut-down of all cooling devices. The validity of the criterion is checked with the help of detailed numerical simulations.Comment: REVTeX, 11 pages, 4 figures; submitted to PR

Goos-Haenchen induced vector eigenmodes in a dome cavity

We demonstrate numerically calculated electromagnetic eigenmodes of a 3D dome cavity resonator that owe their shape and character entirely to the Goos-Haenchen effect. The V-shaped modes, which have purely TE or TM polarization, are well described by a 2D billiard map with the Goos-Haenchen shift included. A phase space plot of this augmented billiard map reveals a saddle-node bifurcation; the stable periodic orbit that is created in the bifurcation corresponds to the numerically calculated eigenmode, dictating the angle of its "V". A transition from a fundamental Gaussian to a TM V mode has been observed as the cavity is lengthened to become nearly hemispherical.Comment: 4 pages, 4 figure

Fractal templates in the escape dynamics of trapped ultracold atoms

We consider the dynamic escape of a small packet of ultracold atoms launched from within an optical dipole trap. Based on a theoretical analysis of the underlying nonlinear dynamics, we predict that fractal behavior can be seen in the escape data. This data would be collected by measuring the time-dependent escape rate for packets launched over a range of angles. This fractal pattern is particularly well resolved below the Bose-Einstein transition temperature--a direct result of the extreme phase space localization of the condensate. We predict that several self-similar layers of this novel fractal should be measurable and we explain how this fractal pattern can be predicted and analyzed with recently developed techniques in symbolic dynamics.Comment: 11 pages with 5 figure