Hyperbolic outer billiards : a first example

We present the first example of a hyperbolic outer billiard. More precisely we construct a one parameter family of examples which in some sense correspond to the Bunimovich billiards.Comment: 11 pages, 8 figures, to appear in Nonlinearit

Students’ view of Quantum Information Technologies, part 2

The aim of the paper is to show how graduatedengineering students in classical ICT view practically the advent ofthe QIT. The students do their theses in El.Eng. and ICT and wereasked how to implement now or in the future the QIT in theircurrent or future work. Most of them have strictly defined researchtopics and in some cases the realization stage is advanced. Thus,most of the potential QIT application areas are defined and quitenarrow. In such a case, the issue to be considered is theincorporation of QIT components and interfaces into the existingICT infrastructure, software and hardware alike, and propose asolution as a reasonable functional hybrid system. The QITcomponents or circuits are not standalone in most cases, theyshould be somehow incorporated into existing environment, with ameasurable added value. Not an easy task indeed. We have toexcuse the students if the proposed solutions are not ripe enough.The exercise was proposed as an on-purpose publicationworkshop, related strictly to the fast and fascinating developmentof the QIT. The paper is a continuation of publishing exercises withprevious groups of students participating in QIT lectures

Acceleration of bouncing balls in external fields

We introduce two models, the Fermi-Ulam model in an external field and a one dimensional system of bouncing balls in an external field above a periodically oscillating plate. For both models we investigate the possibility of unbounded motion. In a special case the two models are equivalent

Entropy production in Gaussian thermostats

We show that an arbitrary Anosov Gaussian thermostat on a surface is dissipative unless the external field has a global potential

Lyapunov Exponent Pairing for a Thermostatted Hard-Sphere Gas under Shear in the Thermodynamic Limit

We demonstrate why for a sheared gas of hard spheres, described by the SLLOD equations with an iso-kinetic Gaussian thermostat in between collisions, deviations of the conjugate pairing rule for the Lyapunov spectrum are to be expected, employing a previous result that for a large number of particles $N$, the iso-kinetic Gaussian thermostat is equivalent to a constant friction thermostat, up to $1/\sqrt{N}$ fluctuations. We also show that these deviations are at most of the order of the fourth power in the shear rate.Comment: 4 pages, to appear in Rapid Comm., Phys. Rev.

Infinitesimal Lyapunov functions for singular flows

We present an extension of the notion of infinitesimal Lyapunov function to singular flows, and from this technique we deduce a characterization of partial/sectional hyperbolic sets. In absence of singularities, we can also characterize uniform hyperbolicity. These conditions can be expressed using the space derivative DX of the vector field X together with a field of infinitesimal Lyapunov functions only, and are reduced to checking that a certain symmetric operator is positive definite at the tangent space of every point of the trapping region.Comment: 37 pages, 1 figure; corrected the statement of Lemma 2.2 and item (2) of Theorem 2.7; removed item (5) of Theorem 2.7 and its wrong proof since the statement of this item was false; corrected items (1) and (2) of Theorem 2.23 and their proofs. Included Example 6 on smooth reduction of families of quadratic forms. The published version in Math Z journal needs an errat

Breaking conjugate pairing in thermostatted billiards by magnetic field

We demonstrate that in the thermostatted three-dimensional Lorentz gas the symmetry of the Lyapunov spectrum can be broken by adding to the system an external magnetic field not perpendicular to the electric field. For perpendicular field vectors, there is a Hamiltonian reformulation of the dynamics and the conjugate pairing rule still holds. This indicates that symmetric Lyapunov spectra has nothing to do with time reversal symmetry or reversibility; instead, it seems to be related to the existence of a Hamiltonian connection.Comment: 4 pages, 3 figure

Linear stability in billiards with potential

A general formula for the linearized Poincar\'e map of a billiard with a potential is derived. The stability of periodic orbits is given by the trace of a product of matrices describing the piecewise free motion between reflections and the contributions from the reflections alone. For the case without potential this gives well known formulas. Four billiards with potentials for which the free motion is integrable are treated as examples: The linear gravitational potential, the constant magnetic field, the harmonic potential, and a billiard in a rotating frame of reference, imitating the restricted three body problem. The linear stability of periodic orbits with period one and two is analyzed with the help of stability diagrams, showing the essential parameter dependence of the residue of the periodic orbits for these examples.Comment: 22 pages, LaTex, 4 Figure

Ultra-high resolution Fourier domain optical coherence tomography for old master paintings

In the last 10 years, Optical Coherence Tomography (OCT) has been successfully applied to art conservation, history and archaeology. OCT has the potential to become a routine non-invasive tool in museums allowing cross-section imaging anywhere on an intact object where there are no other methods of obtaining subsurface information. While current commercial OCTs have shown potential in this field, they are still limited in depth resolution (> 4 μm in paint and varnish) compared to conventional microscopic examination of sampled paint cross-sections (~1 μm). An ultrahigh resolution fiber-based Fourier domain optical coherence tomography system with a constant axial resolution of 1.2 μm in varnish or paint throughout a depth range of 1.5 mm has been developed. While Fourier domain OCT of similar resolution has been demonstrated recently, the sensitivity roll-off of some of these systems are still significant. In contrast, this current system achieved a sensitivity roll-off that is less than 2 dB over a 1.2 mm depth range with an incident power of ~1 mW on the sample. The high resolution and sensitivity of the system makes it convenient to image thin varnish and glaze layers with unprecedented contrast. The non-invasive 'virtual' cross-section images obtained with the system show the thin varnish layers with similar resolution in the depth direction but superior clarity in the layer interfaces when compared with conventional optical microscope images of actual paint sample cross-sections obtained microdestructively

Single-shot two-dimensional full-range optical coherence tomography achieved by dispersion control

We present a full-range Fourier-domain optical coherence tomography (OCT) system that is capable of acquiring two-dimensional images of living tissue in a single shot. By using line illumination of the sample in combination with a two-dimensional imaging spectrometer, 1040 depth scans are performed simultaneously on a sub-millisecond timescale. Furthermore, we demonstrate an easy and flexible real-time single-shot technique for full-range (complex-conjugate cancelled) OCT imaging that is compatible with both two-dimensional as well as ultrahighresolution OCT. By implementing a dispersion imbalance between reference and sample arms of the interferometer, we eliminate the complex-conjugate signal through numerical dispersion compensation, effectively increasing the useful depth range by a factor of two. The system allows us to record 6.7 × 3.2 mm images at 5 μm depth resolution in 0.2 ms. Data postprocessing requires only 4 s. We demonstrate the capability of our system by imaging the anterior chamber of a mouse eye in vitro, as well as human skin in vivo. © 2009 Optical Society of America