Wave Mechanics of Two Hard Core Quantum Particles in 1-D Box

The wave mechanics of two impenetrable hard core particles in 1-D box is analyzed. Each particle in the box behaves like an independent entity represented by a {\it macro-orbital} (a kind of pair waveform). While the expectation value of their interaction, $$, vanishes for every state of two particles, the expectation value of their relative separation,$$, satisfies $\ge \lambda/2$ (or $q \ge \pi/d$, with $2d = L$ being the size of the box). The particles in their ground state define a close-packed arrangement of their wave packets (with $= \lambda/2$, phase position separation $\Delta\phi = 2\pi$ and momentum $|q_o| = \pi/d$) and experience a mutual repulsive force ({\it zero point repulsion}) $f_o = h^2/2md^3$ which also tries to expand the box. While the relative dynamics of two particles in their excited states represents usual collisional motion, the same in their ground state becomes collisionless. These results have great significance in determining the correct microscopic understanding of widely different many body systems.Comment: 12 pages, no figur

Measurement of residual stress by using focused ion beam and digital image correlation method in thin-sized wires used for steel cords

Residual stress in the axial direction of the steel wires has been measured by using a method based on the combination of the focused ion beam (FIB) milling and digital image correlation software. That is, the residual stress was calculated from the measured displacement field before and after the introduction of a slot along the steel wires. The displacement was obtained by the digital correlation analysis of high-resolution scanning electron micrographs, while the slot was introduced by FIB milling with low energy beam. The fitting of the experimental results to an analytical model with the independent Young's modulus determined allows us to find the residual stress. The complete experimental procedures are described and its feasibilities are also evaluated for the thin-sized steel wires.open112sciescopu

Distributed H∞-consensus filtering in sensor networks with multiple missing measurements: The finite-horizon case

The official published version of the article can be found at the link below.This paper is concerned with a new distributed H∞-consensus filtering problem over a finite-horizon for sensor networks with multiple missing measurements. The so-called H∞-consensus performance requirement is defined to quantify bounded consensus regarding the filtering errors (agreements) over a finite-horizon. A set of random variables are utilized to model the probabilistic information missing phenomena occurring in the channels from the system to the sensors. A sufficient condition is first established in terms of a set of difference linear matrix inequalities (DLMIs) under which the expected H∞-consensus performance constraint is guaranteed. Given the measurements and estimates of the system state and its neighbors, the filter parameters are then explicitly parameterized by means of the solutions to a certain set of DLMIs that can be computed recursively. Subsequently, two kinds of robust distributed H∞-consensus filters are designed for the system with norm-bounded uncertainties and polytopic uncertainties. Finally, two numerical simulation examples are used to demonstrate the effectiveness of the proposed distributed filters design scheme.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

Quantum Entanglement of Identical Particles

We consider entanglement in a system of fixed number of identical particles. Since any operation should be symmetrized over all the identical particles and there is the precondition that the spatial wave functions overlap, the meaning of identical-particle entanglement is fundamentally different from that of distinguishable particles. The identical-particle counterpart of the Schmidt basis is shown to be the single-particle basis in which the one-particle reduced density matrix is diagonal. But it does not play a special role in the issue of entanglement, which depends on the single-particle basis chosen. The nonfactorization due to (anti)symmetrization is naturally excluded by using the (anti)symmetrized basis or, equivalently, the particle number representation. The natural degrees of freedom in quantifying the identical-particle entanglement in a chosen single-particle basis are occupation numbers of different single particle basis states. The entanglement between effectively distinguishable spins is shown to be a special case of the occupation-number entanglement.Comment: 5 pages, revtex4. A sentence is improve

Temperature-dependent Raman spectroscopy in BaRuO3_3 systems

We investigated the temperature-dependence of the Raman spectra of a nine-layer BaRuO$_3$ single crystal and a four-layer BaRuO$_3$ epitaxial film, which show pseudogap formations in their metallic states. From the polarized and depolarized spectra, the observed phonon modes are assigned properly according to the predictions of group theory analysis. In both compounds, with decreasing temperature, while $A_{1g}$ modes show a strong hardening, $E_g$ (or $E_{2g}$) modes experience a softening or no significant shift. Their different temperature-dependent behaviors could be related to a direct Ru metal-bonding through the face-sharing of RuO$_6$. It is also observed that another $E_{2g}$ mode of the oxygen participating in the face-sharing becomes split at low temperatures in the four layer BaRuO$_3$. And, the temperature-dependence of the Raman continua between 250 $\sim$ 600 cm$^{-1}$ is strongly correlated to the square of the plasma frequency. Our observations imply that there should be a structural instability in the face-shared structure, which could be closely related to the pseudogap formation of BaRuO$_3$ systems.Comment: 8 pages, 6 figures. to be published in Phys. Rev.

Signature inversion -- manifestation of drift of the rotational axis in triaxial nuclei

A possible scheme of realizing shell model calculations for heavy nuclei is based on a deformed basis and the projection technique. Here we present a new development for odd-odd nuclei, in which one starts with triaxially-deformed multi-quasi-particle configurations, builds the shell-model space through exact three-dimensional angular-momentum-projection, and diagonalizes a two-body Hamiltonian in this space. The model enables us to study the old problem of signature inversion from a different view. With an excellent reproduction of the experimental data in the mass-130 region, the results tend to interpret the phenomenon as a manifestation of dynamical drift of the rotational axis with presence of axial asymmetry in these nuclei.Comment: 10 pages, 5 figure

Modelling a preference-based index for EQ-5D-3L and EQ-5D-3L + Sleep using a Bayesian framework

Background Conventionally, frequentist approach has been used to model health state valuation data. Recently, researchers started to explore the use of Bayesian methods in this area. Objectives This paper presents an alternative approach to modelling health state valuation data of the EQ-5D-3L and EQ-5D-3L + Sleep descriptive systems, using a Bayesian framework, and demonstrates its superiority to conventional frequentist methods. Methods The valuation study is composed of 18 EQ-5D-3L health states and 18 EQ-5D-3L + Sleep health states valued by 160 members of the general public in South Yorkshire, UK, using the time tradeo-ff technique. Three different models were developed for EQ-5D-3L and EQ-5D-3L + Sleep accordingly using Bayesian Markov chain Monte Carlo simulation methods. Bayesian methods were applied to models fitted included a linear regression, random effect and random effect with covariates. The models are compared based on their predictive performance using mean predictions, root mean squared error (RMSE) and deviance information criterion (DIC). All analyses were performed using Bayesian Markov chain Monte Carlo simulation methods. Results The random effects with covariates model performs best under all criterions for the two preference-based measures, with RMSE (0.037) and DIC (637.5) for EQ-5D-3L and RMSE (0.019), DIC (416.4) for EQ-5D + Sleep. Compared with models previously estimated using frequentist approach, the Bayesian models reported in this paper provided better predictions of observed values. Conclusion Bayesian methods provide a better way to model EQ-5D-3L valuation data with and without a sleep ‘bolt-on’ and provide a more flexible in characterizing the full range of uncertainty inherent in these estimates

Density Matrix in Quantum Mechanics and Distinctness of Ensembles Having the Same Compressed Density Matrix

We clarify different definitions of the density matrix by proposing the use of different names, the full density matrix for a single-closed quantum system, the compressed density matrix for the averaged single molecule state from an ensemble of molecules, and the reduced density matrix for a part of an entangled quantum system, respectively. We show that ensembles with the same compressed density matrix can be physically distinguished by observing fluctuations of various observables. This is in contrast to a general belief that ensembles with the same compressed density matrix are identical. Explicit expression for the fluctuation of an observable in a specified ensemble is given. We have discussed the nature of nuclear magnetic resonance quantum computing. We show that the conclusion that there is no quantum entanglement in the current nuclear magnetic resonance quantum computing experiment is based on the unjustified belief that ensembles having the same compressed density matrix are identical physically. Related issues in quantum communication are also discussed.Comment: 26 pages. To appear in Foundations of Physics, 36 (8), 200