On the Conductance Sum Rule for the Hierarchical Edge States of the Fractional Quantum Hall Effect

The conductance sum rule for the hierarchical edge channel currents of a Fractional Quantum Hall Effect state is derived analytically within the Haldane-Halperin hierarchy scheme. We provide also an intuitive interpretation for the hierarchical drift velocities of the edge excitations.Comment: 11 pages, no figure, Revtex 3.0, IC/93/329, ASITP-93-5

Magnetic coupling of a rotating black hole with its surrounding accretion disk

Effects of magnetic coupling (MC) of a rotating black hole (BH) with its surrounding accretion disk are discussed in detail in the following aspects: (i) The mapping relation between the angular coordinate on the BH horizon and the radial coordinate on the disk is modified based on a more reasonable configuration of magnetic field, and a condition for coexistence of the Blandford-Znajek (BZ) and the MC process is derived. (ii) The transfer direction of energy and angular momentum in MC process is described equivalently by the co-rotation radius and by the flow of electromagnetic angular momentum and redshifted energy, where the latter is based on an assumption that the theory of BH magnetosphere is applicable to both the BZ and MC processes. (iii) The profile of the current on the BH horizon and that of the current density flowing from the magnetosphere onto the horizon are given in terms of the angular coordinate of the horizon. It is shown that the current on the BH horizon varies with the latitude of the horizon and is not continuous at the angular boundary between the open and closed magnetic field lines. (iv) The MC effects on disk radiation are discussed, and a very steep emissivity is produced by MC process, which is consistent with the recent XMM-Newton observation of the nearby bright Seyfert 1 galaxy MCG-6-30-15 by a variety of parameters of the BH-disk system.Comment: 24 pages, 19 figures. Accepted by Ap

Screw instability of the magnetic field connecting a rotating black hole with its surrounding disk

Screw instability of the magnetic field connecting a rotating black hole (BH) with its surrounding disk is discussed based on the model of the coexistence of the Blandford-Znajek (BZ) process and the magnetic coupling (MC) process (CEBZMC). A criterion for the screw instability with the state of CEBZMC is derived based on the calculations of the poloidal and toroidal components of the magnetic field on the disk. It is shown by the criterion that the screw instability will occur, if the BH spin and the power-law index for the variation of the magnetic field on the disk are greater than some critical values. It turns out that the instability occurs outside some critical radii on the disk. It is argued that the state of CEBZMC always accompanies the screw instability. In addtition, we show that the screw instability contributes only a small fraction of magnetic extraction of energy from a rotating BH.Comment: 18 pages, 13 figures; Accepted by Ap

An improved differential evolution algorithm and its applications to orbit design

Differential Evolution (DE) is a basic and robust evolutionary strategy that has been applied to determining the global optimum for complex optimization problems[1–5]. It was introduced in 1995 by Storn and Price [1] and has been successfully applied to optimization problems including nonlinear, non-differentiable, non-convex, and multi-model functions. DE algorithms show good convergence, high-reliability, simplicity, and a reduced number of controllable parameters [2]. Olds and Kluever [3] applied DE to an interplanetary trajectory optimization problem and demonstrated the effectiveness of DE to produce rapid solutions. Madavan [4] discussed various modifications to the DE algorithm, improved its computational efficiency, and applied it to aerodynamic shape optimization problems. DE algorithms are easy to use, as they require only a few robust control variables, which can be drawn from a well-defined numerical interval. However, the existing various DE algorithms also have limitations, being susceptible to instability and getting trapped into local optima[2]. Notable effort has been spent addressing this by coupling DE algorithms with other optimization algorithms (for example, Self Organizing Maps (SOM) [6], Dynamic Hill Climbing (DHC) [7], Neural Networks (NN) [7], Particle Swarm Optimization (PSO) [8]). In these cases, the additional algorithm is used as an additional loop within the optimization process, creating a hybrid system with an inner and outer loop. Such hybrid algorithms are inherently more complex and so the computation cost is increased. Attempting to address this, a self-adaptive DE was designed and applied to the orbit design problem for prioritized multiple targets by Chen[5]. However, the self-adaptive feature is somewhat limited as it relates only to the number of generations within the optimization. A Self-adaptive DE which can automatically adapt its learning strategies and the associated parameters during the evolving procedure was proposed by Qin and Suganthan[9] and 25 test functions were used to verify the algorithm

Current-oscillator correlation and Fano factor spectrum of quantum shuttle with finite bias voltage and temperature

A general master equation is derived to describe an electromechanical single-dot transistor in the Coulomb blockade regime. In the equation, Fermi distribution functions in the two leads are taken into account, which allows one to study the system as a function of bias voltage and temperature of the leads. Furthermore, we treat the coherent interaction mechanism between electron tunneling events and the dynamics of excited vibrational modes. Stationary solutions of the equation are numerically calculated. We show current through the oscillating island at low temperature appears step like characteristics as a function of the bias voltage and the steps depend on mean phonon number of the oscillator. At higher temperatures the current steps would disappear and this event is accompanied by the emergence of thermal noise of the charge transfer. When the system is mainly in the ground state, zero frequency Fano factor of current manifests sub-Poissonian noise and when the system is partially driven into its excited states it exhibits super-Poissonian noise. The difference in the current noise would almost be removed for the situation in which the dissipation rate of the oscillator is much larger than the bare tunneling rates of electrons.Comment: 14 pages, 8 figure