Perturbation theory of von Neumann Entropy

In quantum information theory, von Neumann entropy plays an important role. The entropies can be obtained analytically only for a few states. In continuous variable system, even evaluating entropy numerically is not an easy task since the dimension is infinite. We develop the perturbation theory systematically for calculating von Neumann entropy of non-degenerate systems as well as degenerate systems. The result turns out to be a practical way of the expansion calculation of von Neumann entropy.Comment: 7 page

Ground resonance analysis using a substructure modeling approach

A convenient and versatile procedure for modeling and analyzing ground resonance phenomena is described and illustrated. A computer program is used which dynamically couples differential equations with nonlinear and time dependent coefficients. Each set of differential equations may represent a component such as a rotor, fuselage, landing gear, or a failed damper. Arbitrary combinations of such components may be formulated into a model of a system. When the coupled equations are formed, a procedure is executed which uses a Floquet analysis to determine the stability of the system. Illustrations of the use of the procedures along with the numerical examples are presented

Dielectric Breakdown Strength of Polyethylene Nanocomposites

The term “nanometric dielectrics” or simply “nanodielectrics” was introduced in 1994 when Lewis [1] anticipated the potential property changes that would benefit electrical insulation due to nano-sized inclusion. Such materials, containing homogenous dispersion of small amount (normally less than 10wt%) of nanoparticles (with at least one dimension in nanometre range) in host matrix, are of specific dielectric interest. Although much effort has been put forth to investigate the potential dielectric benefit of such newly emerging materials, many uncertainties remain unanswered, and much remains to be explored [2]. Current experimental work is to investigate the preparation of nanodielectrics via solution blending approach. Polyethylene blend composed of 20wt% of high density polyethylene (HDPE) in low density polyethylene (LDPE) is proposed as the base polymer, with varying content of nanosilica (between 0wt% and 10wt%) as the fillers. Although expensive, solution blending method, when compared with melt compounding method, is expected to provide better dispersion of nanoparticles in polymers, thus providing qualitative data in understanding the behaviour of nanodielectrics [3]. Upon successful preparation of polyethylene nanocomposites, breakdown strength based on ASTM Standard D149-87 is to be conducted to determine the feasibility of such dielectric materials in engineering point of view. Figure 1 illustrates the schematic diagram of the breakdown test configuration. The samples are placed between two 6.3mm diameter steel ball bearings immersed in silicone fluid. AC voltage at a preset ramp rate will be applied until the samples fail and the values of breakdown voltages will be recorded and analysed using two-parameter Weibull distribution. Based upon top-down research approach, the underlying physics and chemistry associated with dielectric property changes will then be explored

Development of displacement- and frequency-noise-free interferometer in 3-D configuration for gravitational wave detection

The displacement- and frequency-noise-free interferometer (DFI) is a multiple laser interferometer array for gravitational wave detection free from both the displacement noise of optics and laser frequency noise. So far, partial experimental demonstrations of DFI have been done in 2-D table top experiments. In this paper, we report the complete demonstration of a 3-D DFI. The DFI consists of four Mach-Zehnder interferometers with four mirrors and two beamsplitters. The displacement noises both of mirrors and beamsplitters were suppressed by up to 40 dB. The non-vanishing DFI response to a gravitational wave was successfully confirmed using multiple electro-optic modulators and computing methods

Perturbational approach to the quantum capacity of additive Gaussian quantum channel

For a quantum channel with additive Gaussian quantum noise, at the large input energy side, we prove that the one shot capacity is achieved by the thermal noise state for all Gaussian state inputs, it is also true for non-Gaussian input in the sense of first order perturbation. For a general case of $n$ copies input, we show that up to first order perturbation, any non-Gaussian perturbation to the product thermal state input has a less quantum information transmission rate when the input energy tend to infinitive.Comment: 5 page

Convergence of the Poincare Constant

The Poincare constant R(Y) of a random variable Y relates the L2 norm of a function g and its derivative g'. Since R(Y) - Var(Y) is positive, with equality if and only if Y is normal, it can be seen as a distance from the normal distribution. In this paper we establish a best possible rate of convergence of this distance in the Central Limit Theorem. Furthermore, we show that R(Y) is finite for discrete mixtures of normals, allowing us to add rates to the proof of the Central Limit Theorem in the sense of relative entropy.Comment: 11 page

Markov bases and subbases for bounded contingency tables

In this paper we study the computation of Markov bases for contingency tables whose cell entries have an upper bound. In general a Markov basis for unbounded contingency table under a certain model differs from a Markov basis for bounded tables. Rapallo, (2007) applied Lawrence lifting to compute a Markov basis for contingency tables whose cell entries are bounded. However, in the process, one has to compute the universal Gr\"obner basis of the ideal associated with the design matrix for a model which is, in general, larger than any reduced Gr\"obner basis. Thus, this is also infeasible in small- and medium-sized problems. In this paper we focus on bounded two-way contingency tables under independence model and show that if these bounds on cells are positive, i.e., they are not structural zeros, the set of basic moves of all $2 \times 2$ minors connects all tables with given margins. We end this paper with an open problem that if we know the given margins are positive, we want to find the necessary and sufficient condition on the set of structural zeros so that the set of basic moves of all $2 \times 2$ minors connects all incomplete contingency tables with given margins.Comment: 22 pages. It will appear in the Annals of the Institution of Statistical Mathematic