Symmetries of Discrete Dynamical Systems Involving Two Species

The Lie point symmetries of a coupled system of two nonlinear differential-difference equations are investigated. It is shown that in special cases the symmetry group can be infinite dimensional, in other cases up to 10 dimensional. The equations can describe the interaction of two long molecular chains, each involving one type of atoms.Comment: 40 pages, no figures, typed in AMS-LaTe

Asymmetries in ozone depressions between the polar stratospheres following a solar proton event

Ozone depletions in the polar stratosphere during the energetic solar proton event on 4 August 1972 were observed by the backscattered ultraviolet (BUV) experiments on the Nimbus 4 satellite. The observed ozone contents, the ozone depressions and their temporal variations above the 4 mb level exhibited distinct asymmetries between the northern and southern hemispheres. Since the ozone destroying solar particles precipitate rather symmetrically into the two polar atmospheres, due to the geomagnetic dipole field, it is suggested that these asymmetries may be explained in terms of the differences in dynamics between the summer and the winter polar atmospheres. In the summer (northern) hemisphere, the stratospheric and mesospheric ozone depletion and recovery are smooth functions of time due to the preponderance of undistributed orderly flow in this region. On the other hand, the temporal variation of the upper stratospheric ozone in the winter polar atmosphere (southern hemisphere) exhibits large amplitude irregularities. These characteristic differences between the two polar atmospheres are also evident in the vertical distributions of temperatures and winds observed by balloons and rocket soundings

Robust and Scalable Scheme to Generate Large-Scale Entanglement Webs

We propose a robust and scalable scheme to generate an $N$-qubit $W$ state among separated quantum nodes (cavity-QED systems) by using linear optics and postselections. The present scheme inherits the robustness of the Barrett-Kok scheme [Phys. Rev. A {\bf 71}, 060310(R) (2005)]. The scalability is also ensured in the sense that an arbitrarily large $N$-qubit $W$ state can be generated with a quasi-polynomial overhead $\sim 2^{O[(\log_2 N)^2]}$. The process to breed the $W$ states, which we introduce to achieve the scalability, is quite simple and efficient, and can be applied for other physical systems.Comment: 5 pages, 3 figure

Broadband method for precise microwave spectroscopy of superconducting thin films near the critical temperature

We present a high-resolution microwave spectrometer to measure the frequency-dependent complex conductivity of a superconducting thin film near the critical temperature. The instrument is based on a broadband measurement of the complex reflection coefficient, $S_{\rm 11}$, of a coaxial transmission line, which is terminated to a thin film sample with the electrodes in a Corbino disk shape. In the vicinity of the critical temperature, the standard calibration technique using three known standards fails to extract the strong frequency dependence of the complex conductivity induced by the superconducting fluctuations. This is because a small unexpected difference between the phase parts of $S_{\rm 11}$ for a short and load standards gives rise to a large error in the detailed frequency dependence of the complex conductivity near the superconducting transition. We demonstrate that a new calibration procedure using the normal-state conductivity of a sample as a load standard resolves this difficulty. The high quality performance of this spectrometer, which covers the frequency range between 0.1 GHz and 10 GHz, the temperature range down to 10 K, and the magnetic field range up to 1 T, is illustrated by the experimental results on several thin films of both conventional and high temperature superconductors.Comment: 13 pages, 14 figure

Creation of the universe with a stealth scalar field

The stealth scalar field is a non-trivial configuration without any back-reaction to geometry, which is characteristic for non-minimally coupled scalar fields. Studying the creation probability of the de Sitter universe with a stealth scalar field by the Hartle and Hawking's semi-classical method, we show that the effect of the stealth field can be significant. For the class of scalar fields we consider, creation with a stealth field is possible for a discrete value of the coupling constant and its creation probability is always less than that with a trivial scalar field. However, those creation rates can be almost the same depending on the parameters of the theory.Comment: 7 pages; v2, references added; v3, creation of the open universe adde

Discrete derivatives and symmetries of difference equations

We show on the example of the discrete heat equation that for any given discrete derivative we can construct a nontrivial Leibniz rule suitable to find the symmetries of discrete equations. In this way we obtain a symmetry Lie algebra, defined in terms of shift operators, isomorphic to that of the continuous heat equation.Comment: submitted to J.Phys. A 10 Latex page