Statistics of Chaotic Resonances in an Optical Microcavity

Distributions of eigenmodes are widely concerned in both bounded and open systems. In the realm of chaos, counting resonances can characterize the underlying dynamics (regular vs. chaotic), and is often instrumental to identify classical-to-quantum correspondence. Here, we study, both theoretically and experimentally, the statistics of chaotic resonances in an optical microcavity with a mixed phase space of both regular and chaotic dynamics. Information on the number of chaotic modes is extracted by counting regular modes, which couple to the former via dynamical tunneling. The experimental data are in agreement with a known semiclassical prediction for the dependence of the number of chaotic resonances on the number of open channels, while they deviate significantly from a purely random-matrix-theory-based treatment, in general. We ascribe this result to the ballistic decay of the rays, which occurs within Ehrenfest time, and importantly, within the timescale of transient chaos. The present approach may provide a general tool for the statistical analysis of chaotic resonances in open systems.Comment: 5 pages, 5 figures, and a supplemental informatio

Applicability of the Friedberg-Lee-Zhao method

Friedberg, Lee and Zhao proposed a method for effectively evaluating the eigenenergies and eigen wavefunctions of quantum systems. In this work, we study several special cases to investigate applicability of the method. Concretely, we calculate the ground-state eigenenergy of the Hellmann potential as well as the Cornell potential, and also evaluate the energies of the systems where linear term is added to the Coulomb and harmonic oscillator potentials as a perturbation. The results obtained in this method have a surprising agreement with the traditional method or the numerical results. Since the results in this method have obvious analyticity compared to that in other methods, and because of the simplicity for calculations this method can be applied to solving the Schr\"{o}dinger equation and provides us better understanding of the physical essence of the concerned systems. But meanwhile applications of the FLZ method are restricted at present, especially for certain potential forms, but due to its obvious advantages, it should be further developed.Comment: 14 pages,no figure

Enhanced Reversibility and Durability of a Solid Oxide Fe–Air Redox Battery by Carbothermic Reaction Derived Energy Storage Materials

The recently developed solid oxide metal–air redox battery is a new technology capable of high-rate chemistry. Here we report that the performance, reversibility and stability of a solid oxide iron–air redox battery can be significantly improved by nanostructuring energy storage materials from a carbothermic reaction