Combinatorial identities for binary necklaces from exact ray-splitting trace formulae

Based on an exact trace formula for a one-dimensional ray-splitting system, we derive novel combinatorial identities for cyclic binary sequences (P\'olya necklaces).Comment: 15 page

Exact trace formulae for a class of one-dimensional ray-splitting systems

Based on quantum graph theory we establish that the ray-splitting trace formula proposed by Couchman {\it et al.} (Phys. Rev. A {\bf 46}, 6193 (1992)) is exact for a class of one-dimensional ray-splitting systems. Important applications in combinatorics are suggested.Comment: 14 pages, 3 figure

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

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

Conductance Distribution of a Quantum Dot with Non-Ideal Single-Channel Leads

We have computed the probability distribution of the conductance of a ballistic and chaotic cavity which is connected to two electron reservoirs by leads with a single propagating mode, for arbitrary values of the transmission probability Gamma of the mode, and for all three values of the symmetry index beta. The theory bridges the gap between previous work on ballistic leads (Gamma = 1) and on tunneling point contacts (Gamma << 1). We find that the beta-dependence of the distribution changes drastically in the crossover from the tunneling to the ballistic regime. This is relevant for experiments, which are usually in this crossover regime. ***Submitted to Physical Review B.***Comment: 7 pages, REVTeX-3.0, 4 postscript figures appended as self-extracting archive, INLO-PUB-940607

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

Primäres Chondrosarkom in der weiblichen Brust:Fallbericht und Literaturübersicht

Der Fall einer 77 jährigen Patientin mit einem primären Chondrosarkom der weiblichen Brust wird hier dargestellt. Präoperativ als Mammakarzinom eingeschätzt, zeigte sich postoperativ in der Makro- als auch Mikroskopischen-Untersuchung ein Chondrosarkom. Daher wird zum einen das differentialdiagnostische Spektrum mesenchymaler Weichteiltumoren im allgemeinen und Primären Chondrosarkomen der Mamma im speziellen untersucht und zum anderen die therapeutischen Möglichkeiten und die prognostischen Einschätzungen bei Chondrosarkomen der Brust im Spiegel der Literatur dargestellt. An Fallbeispielen aus der Literatur wird das diagnostische und therapeutische Vorgehen geschildert. Es zeigt sich, dass eine eindeutige präoperative Diagnosestellung eines Chondrosarkoms der Brust ohne Zuhilfenahme von histologischen Untersuchungsmethoden sich schwierig gestaltet

Explicitly solvable cases of one-dimensional quantum chaos

We identify a set of quantum graphs with unique and precisely defined spectral properties called {\it regular quantum graphs}. Although chaotic in their classical limit with positive topological entropy, regular quantum graphs are explicitly solvable. The proof is constructive: we present exact periodic orbit expansions for individual energy levels, thus obtaining an analytical solution for the spectrum of regular quantum graphs that is complete, explicit and exact

Coherent Control of Quantum Chaotic Diffusion

Extensive coherent control over quantum chaotic diffusion using the kicked rotor model is demonstrated and its origin in deviations from random matrix theory is identified. Further, the extent of control in the presence of external decoherence is established. The results are relevant to both areas of quantum chaos and coherent control.Comment: 4 pages, 4 figures, to appear in Phys. Rev. Let

Quantum localization in rough billiards

We study the level spacing statistics p(s) and eigenfunction properties in a billiard with a rough boundary. Quantum effects lead to localization of classical diffusion in the angular momentum space and the Shnirelman peak in p(s) at small s. The ergodic regime with Wigner-Dyson statistics is identified as a function of roughness. Applications for the Q-spoiling in optical resonators are also discussed.Comment: revtex, 4 pages, 5 figure