Symbolic Dynamics Analysis of the Lorenz Equations

Recent progress of symbolic dynamics of one- and especially two-dimensional maps has enabled us to construct symbolic dynamics for systems of ordinary differential equations (ODEs). Numerical study under the guidance of symbolic dynamics is capable to yield global results on chaotic and periodic regimes in systems of dissipative ODEs which cannot be obtained neither by purely analytical means nor by numerical work alone. By constructing symbolic dynamics of 1D and 2D maps from the Poincare sections all unstable periodic orbits up to a given length at a fixed parameter set may be located and all stable periodic orbits up to a given length may be found in a wide parameter range. This knowledge, in turn, tells much about the nature of the chaotic limits. Applied to the Lorenz equations, this approach has led to a nomenclature, i.e., absolute periods and symbolic names, of stable and unstable periodic orbits for an autonomous system. Symmetry breakings and restorations as well as coexistence of different regimes are also analyzed by using symbolic dynamics.Comment: 35 pages, LaTeX, 13 Postscript figures, uses psfig.tex. The revision concerns a bug at the end of hlzfig12.ps which prevented the printing of the whole .ps file from page 2

Ultra-high Q alumina optical microresonators in the UV and blue bands

UV and visible photonics enable applications ranging from spectroscopic sensing to communication and quantum information processing. Photonics structures in these wavelength regimes, however, tend to experience higher loss than their IR counterpart. Particularly in the near-UV band, on-chip optical microresonators have not yet achieved a quality factor beyond 1 million. Here we report ultra-low-loss photonic waveguides and resonators patterned from alumina thin films prepared by a highly scalable atomic layer deposition process. We demonstrate ultra high Q factor of 1.5$\,\times\,$10$^6$ at 390nm, a record value at UV bands, and 1.9$\,\times\,$10$^6$ at 488.5nm

Understanding entangled spins in QED

The stability of two entangled spins dressed by electrons is studied by calculating the scattering phase shifts. The interaction between electrons is interpreted by fully relativistic QED and the screening effect is described phenomenologically in the Debye exponential form $e^{-\alpha r}$. Our results show that if the (Einstein-Podolsky-Rosen-) EPR-type states are kept stable under the interaction of QED, the spatial wave function must be parity-dependent. The spin-singlet state $s=0$ and the polarized state $\frac 1{\sqrt{2}}(\mid +-> -\mid -+>)$ along the z-axis\QTR{bf}{\}give rise to two different kinds of phase shifts\QTR{bf}{.} Interestingly, the interaction between electrons in the spin-singlet pair is found to be attractive. Such an attraction could be very useful when we extract the entangled spins from superconductors. A mechanism to filter the entangled spins is also discussed.Comment: 6 pages, 3 figures. changes adde

Measurement of the branching fractions of psi(2S) -> 3(pi+pi-) and J/psi -> 2(pi+pi-)

Using data samples collected at sqrt(s) = 3.686GeV and 3.650GeV by the BESII detector at the BEPC, the branching fraction of psi(2S) -> 3(pi+pi-) is measured to be [4.83 +- 0.38(stat) +- 0.69(syst)] x 10^-4, and the relative branching fraction of J/psi -> 2(pi+pi-) to that of J/psi -> mu+mu- is measured to be [5.86 +- 0.19(stat) +- 0.39(syst)]% via psi(2S) -> (pi+pi-)J/psi, J/psi -> 2(pi+pi-). The electromagnetic form factor of 3(pi+pi-) is determined to be 0.21 +- 0.02 and 0.20 +- 0.01 at sqrt(s) = 3.686GeV and 3.650GeV, respectively.Comment: 17pages, 7 figures, submitted to Phys. Rev.

Measurements of J/psi decays into phi pi^0, phi eta, and phi eta^prime

Based on 5.8x10^7 J/psi events detected in BESII, the branching fractions of J/psi--> phi eta and phi eta^prime are measured for different eta and eta^prime decay modes. The results are significantly higher than previous measurements. An upper limit on B(J/psi--> phi pi^0) is also obtained.Comment: 9 pages, 10 figure

Observation of p pbar pi^0 and p pbar eta in psi' decays

The processes psi'-->p pbar pi^0 and psi'-->p pbar eta are studied using a sample of 14 million psi' decays collected with the Beijing Spectrometer at the Beijing Electron-Positron Collider. The branching fraction of psi'-->p pbar pi^0 is measured with improved precision as (13.2\pm 1.0\pm 1.5)\times 10^{-5}, and psi'-->p pbar eta is observed for the first time with a branching fraction of (5.8\pm 1.1\pm 0.7)\times 10^{-5}, where the first errors are statistical and the second ones are systematic.Comment: 15 pages, 8 figures and 3 table

Measurement of the chi_{c2} Polarization in psi(2S) to gamma chi_{c2}

The polarization of the chi_{c2} produced in psi(2S) decays into gamma chi_{c2} is measured using a sample of 14*10^6 psi(2S) events collected by BESII at the BEPC. A fit to the chi_{c2} production and decay angular distributions in psi(2S) to gamma chi_{c2}, chi_{c2} to pi pi and KK yields values x=A_1/A_0=2.08+/-0.44 and y=A_2/A_0=3.03 +/-0.66, with a correlation rho=0.92 between them, where A_{0,1,2} are the chi_{c2} helicity amplitudes. The measurement agrees with a pure E1 transition, and M2 and E3 contributions do not differ significantly from zero.Comment: 6 pages, 4 figures, 1 tabl

Modulation of Transmission Spectra of Anodized Alumina Membrane Distributed Bragg Reflector by Controlling Anodization Temperature

We have successfully prepared anodized alumina membrane distributed Bragg reflector (DBR) using electrochemical anodization method. The transmission peak of this distributed Bragg reflector could be easily and effectively modulated to cover almost any wavelength range of the whole visible spectrum by adjusting anodization temperature

Measurements of ψ(2S)\psi(2S) decays into Vector- Tensor final states

Decays of the $\psi(2S)$ into vector plus tensor meson final states have been studied with 14 million $\psi(2S)$ events collected with the BESII detector. Branching fractions of \psi(2S) \rt \omega f_{2}(1270), $\rho a_2(1320)$, $K^*(892)^0\bar{K}^*_2(1430)^0+c.c.$ and $\phi f_2^{\prime}(1525)$ are determined. They improve upon previous BESI results and confirm the violation of the "12%" rule for $\psi(2S)$ decays to VT channels with higher precision.Comment: 7 pages, 7 figures and 2 table

First Measurement of the Branching Ratio of J/ψ→γf2(1270)f2(1270)J/\psi\to\gamma f_{2}(1270) f_{2}(1270)

Using 58 million $J/\psi$ events taken with the BES II detector at the Beijing Electron Positron Collider, a new decay mode $J/\psi\to\gamma f_{2}(1270) f_{2}(1270) \to \gamma \pi^+\pi^-\pi^+\pi^-$ is observed for the first time. The branching ratio is determined to be $Br(J/\psi\to\gamma f_{2}(1270) f_{2}(1270))=(9.5\pm0.7\pm1.6)\times 10^{-4}$, where the quoted errors are statistical and systematic, respectively.Comment: 7 pages, 3 figure