Trace formula for a dielectric microdisk with a point scatterer

Two-dimensional dielectric microcavities are of widespread use in microoptics applications. Recently, a trace formula has been established for dielectric cavities which relates their resonance spectrum to the periodic rays inside the cavity. In the present paper we extend this trace formula to a dielectric disk with a small scatterer. This system has been introduced for microlaser applications, because it has long-lived resonances with strongly directional far field. We show that its resonance spectrum contains signatures not only of periodic rays, but also of diffractive rays that occur in Keller's geometrical theory of diffraction. We compare our results with those for a closed cavity with Dirichlet boundary conditions.Comment: 39 pages, 18 figures, pdflate

Spectral Statistics of "Cellular" Billiards

For a bounded planar domain $\Omega^0$ whose boundary contains a number of flat pieces $\Gamma_i$ we consider a family of non-symmetric billiards $\Omega$ constructed by patching several copies of $\Omega^0$ along $\Gamma_i$'s. It is demonstrated that the length spectrum of the periodic orbits in $\Omega$ is degenerate with the multiplicities determined by a matrix group $G$. We study the energy spectrum of the corresponding quantum billiard problem in $\Omega$ and show that it can be split in a number of uncorrelated subspectra corresponding to a set of irreducible representations $\alpha$ of $G$. Assuming that the classical dynamics in $\Omega^0$ are chaotic, we derive a semiclassical trace formula for each spectral component and show that their energy level statistics are the same as in standard Random Matrix ensembles. Depending on whether ${\alpha}$ is real, pseudo-real or complex, the spectrum has either Gaussian Orthogonal, Gaussian Symplectic or Gaussian Unitary types of statistics, respectively.Comment: 18 pages, 4 figure

Semiclassical universality of parametric spectral correlations

We consider quantum systems with a chaotic classical limit that depend on an external parameter, and study correlations between the spectra at different parameter values. In particular, we consider the parametric spectral form factor $K(\tau,x)$ which depends on a scaled parameter difference $x$. For parameter variations that do not change the symmetry of the system we show by using semiclassical periodic orbit expansions that the small $\tau$ expansion of the form factor agrees with Random Matrix Theory for systems with and without time reversal symmetry.Comment: 18 pages, no figure

Escape Orbits for Non-Compact Flat Billiards

It is proven that, under some conditions on $f$, the non-compact flat billiard $\Omega = \{ (x,y) \in \R_0^{+} \times \R_0^{+};\ 0\le y \le f(x) \}$ has no orbits going {\em directly} to $+\infty$. The relevance of such sufficient conditions is discussed.Comment: 9 pages, LaTeX, 3 postscript figures available at http://www.princeton.edu/~marco/papers/ . Minor changes since previously posted version. Submitted to 'Chaos

Semiclassical expansion of parametric correlation functions of the quantum time delay

We derive semiclassical periodic orbit expansions for a correlation function of the Wigner time delay. We consider the Fourier transform of the two-point correlation function, the form factor $K(\tau,x,y,M)$, that depends on the number of open channels $M$, a non-symmetry breaking parameter $x$, and a symmetry breaking parameter $y$. Several terms in the Taylor expansion about $\tau=0$, which depend on all parameters, are shown to be identical to those obtained from Random Matrix Theory.Comment: 21 pages, no figure

Form factor for large quantum graphs: evaluating orbits with time-reversal

It has been shown that for a certain special type of quantum graphs the random-matrix form factor can be recovered to at least third order in the scaled time \tau using periodic-orbit theory. Two types of contributing pairs of orbits were identified, those which require time-reversal symmetry and those which do not. We present a new technique of dealing with contribution from the former type of orbits. The technique allows us to derive the third order term of the expansion for general graphs. Although the derivation is rather technical, the advantages of the technique are obvious: it makes the derivation tractable, it identifies explicitly the orbit configurations which give the correct contribution, it is more algorithmical and more system-independent, making possible future applications of the technique to systems other than quantum graphs.Comment: 25 pages, 14 figures, accepted to Waves in Random Media (special issue on Quantum Graphs and their Applications). Fixed typos, removed an overly restrictive condition (appendix), shortened introductory section

A critical review of the life sciences project management at Ames Research Center for the Spacelab Mission development test 3

A management study was initiated by ARC (Ames Research Center) to specify Spacelab Mission Development Test 3 activities and problems. This report documents the problems encountered and provides conclusions and recommendations to project management for current and future ARC life sciences projects. An executive summary of the conclusions and recommendations is provided. The report also addresses broader issues relevant to the conduct of future scientific missions under the constraints imposed by the space environment

Scattering induced dynamical entanglement and the quantum-classical correspondence

The generation of entanglement produced by a local potential interaction in a bipartite system is investigated. The degree of entanglement is contrasted with the underlying classical dynamics for a Rydberg molecule (a charged particle colliding on a kicked top). Entanglement is seen to depend on the structure of classical phase-space rather than on the global dynamical regime. As a consequence regular classical dynamics can in certain circumstances be associated with higher entanglement generation than chaotic dynamics. In addition quantum effects also come into play: for example partial revivals, which are expected to persist in the semiclassical limit, affect the long time behaviour of the reduced linear entropy. These results suggest that entanglement may not be a pertinent universal signature of chaos.Comment: Published versio