Poisson Yang-Baxter maps with binomial Lax matrices

A construction of multidimensional parametric Yang-Baxter maps is presented. The corresponding Lax matrices are the symplectic leaves of first degree matrix polynomials equipped with the Sklyanin bracket. These maps are symplectic with respect to the reduced symplectic structure on these leaves and provide examples of integrable mappings. An interesting family of quadrirational symplectic YB maps on $\mathbb{C}^4 \times \mathbb{C}^4$ with $3\times 3$ Lax matrices is also presented.Comment: 22 pages, 3 figure

On Quadrirational Yang-Baxter Maps

We use the classification of the quadrirational maps given by Adler, Bobenko and Suris to describe when such maps satisfy the Yang-Baxter relation. We show that the corresponding maps can be characterized by certain singularity invariance condition. This leads to some new families of Yang-Baxter maps corresponding to the geometric symmetries of pencils of quadrics.Comment: Proceedings of the workshop "Geometric Aspects of Discrete and Ultra-Discrete Integrable Systems" (Glasgow, March-April 2009

Yang-Baxter maps and multi-field integrable lattice equations

A variety of Yang-Baxter maps are obtained from integrable multi-field equations on quad-graphs. A systematic framework for investigating this connection relies on the symmetry groups of the equations. The method is applied to lattice equations introduced by Adler and Yamilov and which are related to the nonlinear superposition formulae for the B\"acklund transformations of the nonlinear Schr\"odinger system and specific ferromagnetic models.Comment: 16 pages, 4 figures, corrected versio

Yang Baxter maps with first degree polynomial 2 by 2 Lax matrices

A family of nonparametric Yang Baxter (YB) maps is constructed by refactorization of the product of two 2 by 2 matrix polynomials of first degree. These maps are Poisson with respect to the Sklyanin bracket. For each Casimir function a parametric Poisson YB map is generated by reduction on the corresponding level set. By considering a complete set of Casimir functions symplectic multiparametric YB maps are derived. These maps are quadrirational with explicit formulae in terms of matrix operations. Their Lax matrices are, by construction, 2 by 2 first degree polynomial in the spectral parameter and are classified by Jordan normal form of the leading term. Nonquadrirational parametric YB maps constructed as limits of the quadrirational ones are connected to known integrable systems on quad graphs

A qq-anaolg of the sixth Painlev\'e equation

A $q$-difference analog of the sixth Painlev\'e equation is presented. It arises as the condition for preserving the connection matrix of linear $q$-difference equations, in close analogy with the monodromy preserving deformation of linear differential equations. The continuous limit and special solutions in terms of $q$-hypergeometric functions are also discussed.Comment: 8 pages, LaTeX file (Two misprints corrected

Fabrication of integrated planar gunn diode and micro-cooler on GaAs substrate

We demonstrate fabrication of an integrated micro cooler with the planar Gunn diode and characterise its performance. First experimental results have shown a small cooling at the surface of the micro cooler. This is first demonstration of an integrated micro-cooler with a planar Gunn diode

Space very long baseline interferometry observations of polarization in the jet of 3C 380

A comparison between low-frequency space very long baseline interferometry (VLBI) and high-frequency ground-based VLBI images can, in principle, be used to detect small variations in rotation measure (RM) on fine angular scales inaccessible to ground arrays alone. This paper reports an attempt to perform such a comparison using the jet in the quasar 3C 380. Observations made with the VSOP antenna HALCA together with a ground array at wavelength 1.6 GHz provide total intensity and polarization images of comparable resolution to those from the ground array alone at 5 GHz. The results provide an image showing derotated magnetic vector position angle of somewhat higher resolution than that available earlier. The results show variations in an RM around component A of the order of 10 rad m(-2) that could not have been detected with the ground array alone. It is concluded that satellite VLBI observations provide a promising means to study the distribution of matter and magnetic fields around parsec-scale jets. The ground observations used here follow the steady outward drift of component A, which has approximately doubled its distance from the core since the first observations in 1982. They also reveal total intensity and polarization structure associated with a bright knot 0.7 arcsec from the core which is reminiscent of that expected for a conical shock wave

Time--Evolving Statistics of Chaotic Orbits of Conservative Maps in the Context of the Central Limit Theorem

We study chaotic orbits of conservative low--dimensional maps and present numerical results showing that the probability density functions (pdfs) of the sum of $N$ iterates in the large $N$ limit exhibit very interesting time-evolving statistics. In some cases where the chaotic layers are thin and the (positive) maximal Lyapunov exponent is small, long--lasting quasi--stationary states (QSS) are found, whose pdfs appear to converge to $q$--Gaussians associated with nonextensive statistical mechanics. More generally, however, as $N$ increases, the pdfs describe a sequence of QSS that pass from a $q$--Gaussian to an exponential shape and ultimately tend to a true Gaussian, as orbits diffuse to larger chaotic domains and the phase space dynamics becomes more uniformly ergodic.Comment: 15 pages, 14 figures, accepted for publication as a Regular Paper in the International Journal of Bifurcation and Chaos, on Jun 21, 201

Microwave saturation of the Rydberg states of electrons on helium

We present measurements of the resonant microwave excitation of the Rydberg energy levels of surface state electrons on superfluid helium. The temperature dependent linewidth agrees well with theoretical predictions and is very small below 300 mK. Absorption saturation and power broadening were observed as the fraction of electrons in the first excited state was increased to 0.49, close to the thermal excitation limit of 0.5. The Rabi frequency was determined as a function of microwave power. The high values of the ratio of the Rabi frequency to linewidth confirm this system as an excellent candidate for creating qubits.Comment: 4 pages, 4 figure

Planar gunn diode characterisation and resonators elements to realise oscillator circuits

The paper describes the planar Gunn diode, which is well suited to providing milli-metric and tera hertz sources using microwave monolithic integrated circuit (MMIC) technologies. Different planar Gunn electrode geometries are described along with DC, RF and thermal characterisation. To realize the planar high frequency sources there is requirement for high frequency planar resonators, the paper will describe both the radial and new diamond shaped geometries